You can go into do-not-disturb mode to stop the flashing, but then pings aren't delivered and you can't do 1-on-1 calls. So there's a pretty significant tradeoff. I wasn't able to find a way to disable them any other way (registry hacks I saw recommended online didn't work).
This sucks because if I see the taskbar flashing, I MUST go and check out Teams. It's too distracting to leave on. So there can't be a background group chat where I'm not taking part and doing other things -- I get dragged into checking every message which is extremely annoying. I suspect that 'immediately check out the app causing the taskbar to flash' is basically a conditioned response for most computer users so I doubt I'm the only one who feels this way.
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I also strongly dislike the vibe of the Teams emoji set. The :) looks like it's playing dumb, and it adds that connotation to messages I see from people using it. (admittedly I've only seen it be used by my dumb coworkers)