Agree as a table that rules discussions happen out-of-session
We have had this issue at our table. Rules debates that have gotten out of hand and players (including and sometimes primarily me in the past) looking up rules and rulings disrupting the session. The following method is what helped our issue a lot:
If any rule is unclear or confusing the DM will make a quick, temporary ruling
during the session (that is binding only for that session). Usually, I rule in
favor of the player especially in cases where it is life-or-death. But at your table you can use
whatever criteria allows you to make a quick decisive ruling that seems fair. Do not allow any argument about this ruling at the table.
Either after this session or before the next one, I will review the
ruling, I'll look at the rules, talk with the player and hear their
arguments and come to a final decision about how the rule will work
going forward. Be fair, and fully consider the player's arguments, then make a ruling. This ruling is considered final.
At some point before a session, let your players know that this will be the way you handle rules disputes going forward. You will not accept any debate during the session but make it clear that you are happy to talk with them before or after. Try to make it clear why you are ruling this way too: rules debate breaks up the story that your group is trying to craft. This rule keeps the fun session going while allowing rules to be addressed at a later time. Ask them to trust you as a DM and to allow you to make a ruling that seems fair and quick in order to keep things fun for everyone. Talk about it and get buy-in from everyone at the table.
An interesting byproduct of this ruling is that players are naturally incentivized to proactively bring up questions they have for rulings before session since they know they can't debate during. This is great for both of us as we can go into the session with an agreed upon ruling (even if I end up disagreeing with the player). Obviously though, this won't work for everything as rules issues are often unexpected.
Declare last call for arguments/issues before the session begins
One specific technique that I have not tested, but seems like it would help in your circumstance was suggested by @philbo in a comment: Simply stop before every session and ask if the players have any rules issues or other topics they wish to discuss before you begin the session.
Explicitly state that this includes any rules arguments that people anticipate. After that, the player is going to look pretty silly trying to spring a pre-planned rules argument mid-session on you and you can simply respond: "I gave you the chance to bring this up at the beginning of the session and you chose not to. Now you have to wait until the end and then we can discuss it."
Being lenient with table rulings helps considerably with trust and buy-in
I have found that it helps a lot to get buy-in and keeping things running smoothly if I lean towards ruling with the player at the table for my temporary rulings. Not always, of course. When you are sure the player's desired ruling is not consistent with the way you adjudicate the rules and the ruling will have a negative effect on the game is about the only time I hard overrule the player at the table. If you tell players that you intend to do this is tells them that you respect their arguments for the rules and trust them (to a point).
It also removes much of the need for arguing during session at all which removes times where the player is fuming or refusing to back down after being overruled. Instead this happens out of session where it doesn't affect game time. Just make a note and review the rule later yourself and if the player was in the "wrong" then talk with them, fully understand their position and make the final ruling out of session. At all times remember to be fair and reasonable with rulings to maintain the players' trust and openly admit if you make a mistake.
What if players keep trying to argue during the session?
Once you have made it clear how and when rules debates happen, simply do not engage in debate during the session. If they start to argue, tell them "I made my ruling, see me after the session and we will talk." If they keep arguing, for example during combat, tell them that if they do not move past it and choose something you will skip their turn.
If you remain firm on the point and don't engage at all, players will soon learn that it is no good to try to argue during the session. At my table, players learned this very quickly and I didn't have to invoke it more than a handful of times.
You have the final say as a DM
It is also probably worth it to remind your players that, in 5e, you as the DM have the final say on rulings at the table and how the rules are interpreted. Remember, there are often multiple ways to read the Rules as Written (RAW) and it is not some monolithic "correct" ruling that is clear. Sometimes the RAW is unclear or even silent on an issue. Sometimes this is even by design, since 5e is designed to be less focused on detailed interactions instead trusting the DM to make the ruling they think will be best for their table.
In the end, tell them that you will always be focused on making things fair and fun, but when you make a decision final you consider it to be done unless new issues crop up. In the end, it is your decision that matters for the table, not Google's, not Jeremy Crawford's1 and not RPG.se's.
In our games implementing this method has vastly cut down in the amount of rules arguing and has improved flow and fun for the whole table. We've played this way under multiple DMs (not just me) and I've also done this as a player. It has worked effectively in each situation. It takes a bit of time to fully work and rules quibbles and issues are never fully eliminated, but it is a vast improvement.
1 - You also might find it helpful to note that you are correct on your stance on designer clarifications. They are not RAW (though they might be a RAW interpretation). And they are often expressing how the game is intended to be run (often called Rules as Intended or RAI). None of which has any binding impact on how you rule at your table. Note also that Crawford tweets are now explicitly unofficial rulings.