Hi, registered just to add to this thread.
This started happening to me a few weeks ago on my 2018 MBP 13", although my situation is a bit different. I get the blinking only upon waking the MBP from a long sleep, although one time it happened when I powered it up first thing in the morning (I don't usually shut down completely). It used to happen once in a while, now it seems to be pretty consistent, and the number of blinks is increasing (this morning, it was 11). So it basically happens as soon as I open the lid or press a key, until I use TouchID to enter my password, although once it kept blinking for awhile even after that. A couple of times, my touch bar became dark and unusuable after the blinking stopped (which a restart did not remedy), with one of those times resulting in a crash after I tried sleeping and waking the MBP (it worked fine after that). Most of the time, it blinks a few times, then everything works normally. If the computer is left idle but not asleep, and the backlights all shut off, it does not happen. The flash covers most of the touch bar, aside from the far left side. It may have been smaller at some point, but not a single square like many others have reported. The flash is very bright, and resembles a camera flash with the way it gradually dims.
The weirdest occurrence though, was one time my MBP was asleep and the lid was open, left this way from the night before. (I was downloading something, and I set it to sleep after the download finished, which was sometime after I had already gone to bed.) When I woke up in the morning, the touch bar was blinking intermittently. Who knows how many times it blinked overnight.
I couldn't reproduce the problem in Safe Mode, but what I need to do is put the MBP in Safe Mode before going to bed, and see if it happens in the morning. I expect it will, because I think it's clearly a hardware issue if it can happen as soon as I press the power key to turn on the MBP.
I could live with a dead touch bar (though I wouldn't like it), except that Apple made the boneheaded decision not to have a mechanical Esc key. (And of course they doubled down on their stupidity by placing the virtual Esc key halfway out of position for the sake of visual symmetry. But I digress...)
I tried to get an estimate from a repair place that isn't an Apple Store, hoping for something less expensive than a full logic board replacement, but the guy never replied.
When I first got this MBP, the battery swelled to the point of bulging the case and causing problems with the keyboard and trackpad. This happened about 19 months after I got it. I got it repaired a few months later, when Apple Stores began opening again. Now this blinking problem has shown up, about 19 months since that repair.
Count me in on a class action. I wish it were possible to replace the touch bar with mechanical function keys, so we can be sure this won't happen again.
EDIT 2022-05-21: Aaaaaaaaand now it appears to be completely dead. Stayed dark after wake and after shutting down and powering up. No crashes though, thank god for that. Better than the blinking, I guess, although changing volume, taking screenshots, and applying multiple tags will require a bit more effort. (Those were pretty much the only things I used the touch bar for, other than the Esc key.)