Interesting how Infotainment crosses into EyeSight for you though. That's not at all what that means.

And yes it beeps and you can't turn the beeping off completely. It's supposed to annoy you into using the blinkers properly. Different cars/model years seem to have different levels of annoyingness in the actual beep and different volume settings available though.

My (also 2020) never beeps when EyeSight can't see the lanes, whether its steering or not. It beeps when you cross a line without blinking or you're crossing the lines and would soon be driving on the shoulder/into the trees. It does sometimes have issues where it beeps a bit too early, i.e. it seems the calculations from the visuals are a bit off in certain situations.