Inasmuch as I try not to prioritize my fun over my players', I also do not prioritize their fun over mine.
Speaking as a frequent DM, my primary "fun" is having engaged players. Their interest in what's going on right now in the game is the best metric I've found for determining whether or not I'm doing a good job as DM (I also like outright compliments and when the players laugh/groan/grind their teeth at my puns!).
I try not to judge (or even characterize) that engagement. It's none of my business. Each player can define the level & kind of immersion they want for themselves. As long as their paying attention & playing nice with each other, we're good.
They're engaged with the metagame. I'd rather they were engaged with the game itself.
How do you define "the game itself", if not as the "the game the real people are really playing"?
The in-game world is a subset of the real world around the table. Playing a game at that table is the real thing; the game. How can it be anything else.
What you're calling "the game itself" is just a preference for a certain mode of play. Which is cool as a statement of preference (hello tautology my old friend...). But it kinda sucks as an attempt at a
definition of the game.
Why must we go there? Look at all that middle you've excluded. The line between "engaged with the game by conferencing combat tactics" and "totally disengaged, looking at phone" is not fine, it's a gulf the size of an ocean.
In my campaigns, that ocean-sized gulf is about five-to-ten minutes.
I wasn't trying to make some crazy exaggerated strawman-point. I was sharing real, personal experience. Players get distracted easily, mainly because of the one-to-many DM-to-player relationship, and it's nice when they aren't. This has been true for as long as I've been gaming. Back it the day it was leafing through rule books or the latest Ray Feist paperback, instead of the omni-distraction that is the contemporary smartphone.
It's that people would tell me what to do on my turn.
Aha... got it! We're not talking about the same thing at all. I thought you were objecting to tactics discussions that couldn't plausibly occur place in-character, during battle. But your issue is with unwanted kibitzing from other players telling you how to play your PC. Yeah, that's rude.
It's, to quote Mal Reynolds,
meddlesome to criticize other players for not valuing immersion in precisely the way you do, but it's a serious breach of etiquette for other players to keep offering unsolicited advice after you've told them to stop. They should respect your preferred playstyle (as you should respect theirs).