I DM for either a pair of players or up to six people out of a ragtag group of friends depending on the week. And all of it happens online, in a friend group where we've only met in person once. Everything that follows is based on my experiences wrangling this particular group of wild monkeys into something approaching a reasonable game.
You may also find some help in some questions I've previously asked or answered.
Talking over each other is the easiest to solve
The funny thing about balancing conversation is that it's actually just as much of a problem in person as it is online. The difference is we can more quickly and easily asses visual cues and give people the space they need to talk in person. This is harder to do online because there's less cues, but they do still exist.
I found the easiest way to move past the issue was just to drag everyone online for a couple hours of Teamspeak and video games here and there. It's a low-pressure situation where people can converse and get used to each others' tells. Almost as often as I run a session for the group I'm setting up Golf With Your Friends tournaments or making a new Don't Starve Together world.
It's maybe a little underhanded but by hosting the games myself I end up being de-facto leader. They're already used to working with me to get whatever they want, and collaborating with each other to achieve tasks to benefit the group. Bottom line: my players get to work together in a situation that requires far less brain power and focus than an actual tabletop game, but is still collaborative. It's good practice for tabletop gaming and still insanely fun!
By the time you have a couple dozen hours of talking time under your collective belts it becomes a lot easier to identify that the little inhale Alice just did means she has something to say, or the way Bob's rambling means he's out of ideas and someone can cut him off without it being rude. You're already used to their ways of typing and it's not much of a leap to start associating that with their ways of talking.
It's also your job as GM to mitigate some of the struggle
You more than anyone should have a sense of who is controlling the table and who hasn't had a chance to talk in a while. If everyone bursts out at once, call on the quietest player.
Depending on your style (and what game you're playing) this can also sometimes be handled mostly in-game. Have NPCs focus on one player talking over the others, or coax a quiet player into talking. There's also rarely harm in just pretending you couldn't understand anyone in the babble and calling on them one by one to get everyone's story.
If it's exceptionally bad at your table you may need to sit down with all of them (or possibly just your particularly loud guys) and ask them to be more respectful of each other, but from the way you phrased things it sounds like this is more accidental than meanspirited.
The brutal truth is not everyone's going to be equally immersed.
Everyone's different and one person's 100% engaged may not look like someone else's. Sometimes we as GMs take players becoming disinterested as a personal affront, but everyone's going to engage differently.
My interpretation of your current situation is that there's two possible root issues, and both may be happening at once. One, you sound like you might be a little burnt out as a group. And two, some of your players may be bored.
Being burnt out
It happens to the best of us. And for your slightly-less-invested players, it can actually happen pretty quickly. I'm talking over the span of a couple of hours. I have one player who, like clockwork, gets less and less involved if any game runs over two hours. Zero shame on her, she just doesn't have the attention span for things. If I sense her withdrawing and speaking up less I know it's time to either call for a snack break to let everyone relax and chat for a bit, or time to end the session for the day.
I also have a player who was a model citizen for the first couple of weeks of play. She was fully invested, interested, and I felt like I had 100% of her attention. Over time however she started slipping, becoming more aggressive and sloppy in her play. I ended up taking her aside and asking what was up and it turned out she was totally burnt out and needed a few weeks away from the table to recharge.
It might be time for your group to take some time off, or to play without a particular player or two while everyone recharges.
Boredom
Is it possible some of your players are bored? I know my roleplay-focused players start to tune out if combat goes on too long and have to called on when it's their turn to roll for attacks. Conversely, I have one player who consistently checks out when everyone else is interrogating NPCs because they struggle with the give-and-take and would rather just hit things.
It's not easy to balance these things, particularly in larger groups, but trying to vary what's going on in the game as much as possible may help a little bit.
It may also be worth sitting down with the most troublesome player(s) and having a little mini session 0 to see if they want/need more out of the game than they're currently getting to keep them invested.
You've been playing a lot longer than I have so you already know this, but it's important not to take anything personally (unless, of course, it actually is personal). Everyone's different and everyone's engagement levels are going to be different.
As a caveat to the above; are you sure they're not as focused as they can be?
I know at least half of our table either plays games on their phones or fiddles with all sorts of little fidget things during play. It's harder to keep your eyes locked on the screen when very little is happening visually and the only stimulus you have is people talking. I myself tend to have to keep my hands busy when I'm a player in someone else's campaign because I'm so used to needing to keep my eyes on a thousand things at once when DMing that the lack of stimulus makes my mind wander.
I agree that if the disengagement is affecting play something has to be done, but everyone's always going to be just a little bit distracted and there's not always anything you can do about it while still being reasonable.
TL:DR;
- Hanging out in a voice channel with the group you GM for outside of the table can help a lot with everyone talking over each other. Practice makes perfect!
- Not everyone will engage the same way, but often a lack of engagement comes from either being burnt out (in the moment, or overall) or boredom with the current story/activity/etc. Checking in with your players and adjusting accordingly can help mitigate it.
