Your group needs to come to an agreement about what makes a fun game.
There are some players/DMs who view D&D as a realistic simulation, looking for the natural progression of events. If you don't set a watch, you may be ambushed during the night and at a lethal disadvantage. You may run into encounters where you are entirely overmatched while not being aware of it. This is a perfectly fine playstyle.
There are some players/DMs who view D&D as a heroic simulation, akin to a movie or high fantasy novel. If you don't set a watch, there may be an ambush during the night but you're not at any particular disadvantage. You may run into encounters where you are entirely overmatched but will be specifically aware of it. This is also a perfectly fine playstyle.
The goal of the game is to have fun.
Your DM seems to be of the first mindset, whereas the rest of you seem to be of the second. You need to come to an agreement somewhere in the middle, where everyone is enjoying what is going on.
Assuming your DM cares about your enjoyment of the game at all, they are undoubtedly having similar concerns about the game -- wanting you to notice the clues, wanting you to make more tactical decisions, etc. It's not fair for their enjoyment to be disregarded, just like it's not fair for your enjoyment to be disregarded.
Most of this requires full DM buy-in; player specific advice follows afterwards because it builds on these items. These all come from my experience in running a number of games (not just D&D). In particular, the philosophy of Dungeon World is strongly represented here.
One note is that absolutely none of this is specific to reconnaissance, and can and should be applied much more generally.
The DM should give more/easier clues. There are a number of well written articles on this, such as The Three Clue Rule, Tips For Creating Good Clues, or Designing A Mystery for DnD, but the general gist is:
- For any given piece of information, there should be multiple (at least three) clues for it. If there is a secret cult in town, there should be at least three clues that might clue you in (as examples, rumors in town about disappearances, cultist villagers using secret signs or having marks, and encountering cultist villagers in the woods with no good reason to be there). If the party needs to find the secret cult's headquarters, that should have at least three other clues (interrogating a captured cultist, following a cultist, or having a villager that has seen strange things). Every step should have multiple possibilities that lead to the next step.
- The DM should calibrate the clues according to the players. Since the DM knows what is going on, many things will be obvious to them that simply are not obvious to the players. Perhaps the DM is using tropes that they expect to be common sense that the players are unfamiliar with. Perhaps the DM is expecting more abstract leaps from the players then the players actually make. But if all of the DM's clues are missed, and this happens repeatedly, the DM needs to consciously make the clues easier to get, no matter how hand-holdy it seems to them.
Players should be prompted for interesting choices, and non-interesting choices should be assumed to be automatic. Take setting a watch: in D&D, there is usually no reason to not set a watch (you don't suffer exhaustion, still receive a long rest, etc), so this shouldn't even be a choice -- your characters are 14th level, and presumably extremely competent, adventurers. Unless there's a reason to not set a watch, it should just be assumed they do so. After all, it is incredibly unlikely you are expected to say things like "I clean and oil my armor" or "I sharpen my sword"; it's just assumed that such things are done.
Similarly, if a rogue or someone else skilled in detecting traps is going down a hallway, if there is no reason for them to not check for traps, they should be assumed to be doing so.
Now, perhaps there is something that makes the choice interesting -- "Are you running down the hall to put distance between you and the orcs, or are you taking it slow and steady to look for traps?" is interesting. "You're all exhausted. Anyone who keeps watch will remain exhausted. Are you going to keep watch?" is interesting.
It is best if these choices are explicitly understood by everyone involved: "when we sleep, we keep these watches," "when the rogue scouts, they check for traps", "when we're not under time pressure we search all rooms," but the DM should give the benefit of the doubt to the party that they are competent and automatically do competent things unless there's a reason otherwise.
Parts of the game that focus on a single player should be minimized. This is a group game, after all, and if a majority of the group is not involved it is probably not enjoyable for them.
Whether or not your wizard casts arcane eye or use a familiar are interesting choices (arcane eye burns a spell slot, the familiar may be killed), but the details of the scouting itself aren't particularly interesting. If the arcane eye maps out the entire dungeon / lair / fortress, then that information can simply be provided; there's no reason to make you, the player, say "I check the next room. I check the next room. I check the room through the right door. I go back and check the room through the left door. I investigate the chest. I investigate the desk. I check the next room" if there's nothing that can interrupt the process. The DM can just give you -- and the rest of the party -- the information and get on with the group portion of the game.
Now, maybe there is something that can interrupt the flow -- then it becomes interesting. But even then it can be minimized -- "the archer sees your owl and shoots it dead," or "the wizard notices your arcane eye, and with dispels it, but now they're aware of the party's presence"
The lethality of consequences should be toned down or the consequences should be made incredibly obvious. Analysis paralysis and the like is due to the belief that if the wrong decision is made, the consequences will be drastic, necessitating spending a lot of time making the right decision.
Analysis paralysis is typically boring for everyone involved, so should be minimized unless the consequences are drastic, in which case it is more or less warranted.
This can be done in one of two ways:
- Making the consequences less drastic. There will be less analysis paralysis if the consequences are not crippling. Starting a party-level-appropriate combat is much less dire than a CR 20 combat (or one where a group of eight mind flayers gets a surprise round) that can potentially wipe the entire party.
- If the consequences are drastic, they should be explicitly communicated to the players. "If you scout the wizard's tower, you can learn the layout but may lose the element of surprise." "If the dragon wakes up while you're carting out its treasure, it's very likely to eat you." "There is an aura of palpable dread surrounding the Ancient Artifact of Doom, and the lich will know when it is moved. Are you sure you want to pick it up?"
The goal should be to both not spend time on small decisions, and to have the information needed to make important decisions. You may still make decisions that you regret, of course, but you'll be making them aware of the consequences, instead of having to worry about the dozen possibilities, eleven of which are not actually going to happen.
(As previously discussed, if there's one path that is consequence free and no reason for the party to take another path, then the decision should just be assumed.)
Player specific advice
This builds off of the previous section, and are things that you can do without complete DM buy-in -- most of them are essentially prompting the DM to do things that they should otherwise be doing. They do require you to be proactive in your statements, however, so there might be a learning curve in terms of when or what you need to prompt the DM for.
State actions that you take automatically. "We always set a watch unless there's a reason not to. We always check for traps unless there's a reason not to. We always search rooms unless there's a reason not to." If necessary, type it out and pin it in your discord channel or equivalent.
If new situations come up that you don't have automatic actions for, and they seem in general to have one superior choice, then add them to the list going forward.
If the DM complains, you can maliciously comply by asking "What are the consequences of not setting a watch?", and upon learning that there are none, saying "We set a watch," but if it takes more than two or three times then there is a larger disconnect.
Ask the DM broad questions for information that your character would be able to determine. This one is difficult because it requires you to be proactive about what you need to ask, but things like "Where is the best place to set an ambush along the trail?", "What are the ways we can sneak into the castle?", or "As a competent adventurer, what are we missing?" It's the DM's job to convey the information of the world to you, and your characters are hopefully competent in setting up ambushes/sneaking into castles/knowing what competent adventurers do, so leverage that.
The goal with these questions is to narrow down a wide set of hypothetical possibilities into just a few paths that the DM has classified as important. Making the questions broad is to avoid asking the same question repeatedly about different subjects.
If the DM is hesitant to give such information (either because they see it as hand-holdy, or because they value player input on path choosing more than you do), then most can be rephrased in the form of an action: "I scout the best place to set an ambush along the trail," "I case the castle for ways in," or "I go through memories of former adventures looking for similarities to this situation."
State broad or general actions. Not "we search the desk" but "we search the entire room." Not "we talk to the drunk at the inn" but "we talk to the villagers." Not "I scout this room with arcane eye" but "I scout the tower with arcane eye."
The goal is to avoid tediousness of saying the same thing over and over, but specifically to avoid the instance of "You said you searched the dresser and the bed, but not the desk, so you didn't find the key." Again, you can maliciously comply if the DM objects by asking "What are all of the objects in the room?" followed by "I search the desk," "I search the rug," "I search the torch," but if this takes more than two or three times there's a disconnect. If there is an actual consequence, the DM will be sure to let you know when you trigger it.
Ask for the consequences. Again, slightly difficult as it requires you to be proactive, but if the group is dithering between two or three actions, ask the DM what the possible consequence of each one is.
If the DM refuses to say, either continue to dither until the DM is bored, or state your opinion and that you're going to read stackexchange until an agreement is made and to let you know when that happens.
Inform the group when you are not having fun. Though the "going to read stackexchange" statement above is facetious, stating when you are not having fun is not. State when you are not having fun, and ask if anyone (including the DM) is. That is, literally asking "I'm not enjoying this. Is anyone enjoying this?" If no one is having fun, then move on to something that is fun.
If multiple players are having fun, it's probably best to let them (their enjoyment is important, too), but you can still indicate your dropping out of the current situation: "We've been talking about this for ten minutes and don't seem to be making progress. I've stated my position, so I'm going to stay silent until a decision is made." If this goes on for a significant time, then indicate your attention is going elsewhere and ask to be pinged when the situation moves on or your involvement is needed.
An alternative is if the DM is having fun, but no player is, to propose a method to easily resolve the conversation: "We've been talking about this for ten minutes and we're deadlocked. Can we just flip a coin and move on?"
 If the DM does not care about your enjoyment as players of the game, that is a separate problem.
 I understand this is not a standard rule in D&D, and it is presented simply as an easily-understood example.
 The malicious compliance is not actually recommended, but more of a facetious take on why this advice is being given, and what following it avoids.