Interesting. I got my M3 December 29th, 2020. The heat failed on the drive home from picking it up (that was a very chilly experience). The next day we got a software update and the following day the heat began working again. I only just got the PT sensors replaced about a month ago, and at that time they also replaced the compressor... they didn't explain why.
Have you had PT sensors replaced on yours?
I have had all the HVAC sensors replaced as well as the compressor already

. I had the exact same issue as you, just a little later in my ownership (around 2k miles), but replacing the sensors didn't fix the issue, nor did any software updates. It's been fine since the compressor was replaced, however. Now that it's getting warmer out, though, I have less opportunities to test.
I would be careful with the sensor replacements. I think they're replacing the failed sensors with the same batches that also are prone to failure. One of the ones they replaced for me failed immediately, and that's when they also decided to swap the compressor. I would also submit a claim to the NHTSA website for your HVAC issues as they need to know that Tesla is knowingly shipping cars with a safety issue in cold climates.
What I'm noticing is a trend with the mid-late December M3s. A lot of similar issues with HVAC and the fit and finish. I will say that if you have a misaligned trunk, keep pressing on the service center to fix it. I took it in a few months ago and they said they couldn't do anything, and on my last visit they actually fixed the issue and it looks much better. I noticed the same thing Sandy Munro did, that it seemed like one side of my car was issue free, and the other side looked like the robots were drunk.