Random rebooting seems to be a "common" Pixel 6 problem. Most were only able to fix it by getting a new device from Google, some were able to fix it with a factory reset.
Strangely enough, I had the same problems on my first Pixel 6 - then I got a replacement model, got the backup from my old phone (p4 xl) going (again) and never had any reboot problems. Then a couple days ago I rooted my Pixel 3 and transfered my files over from my main Pixel 6 Pro and got the same reboot problem on my Pixel 3 now (~about every 10 minutes of active usage). I found out that it's probably connected to the fingerprint scanner, since about every third time that I use the FP on my P3, the phone reboots. I'll probably try a factory reset on my P3, since I know that the phone worked without issue before. It was probably an unwise idea to get a backup from my P6 going, but then again, F*** Google for not giving us a decent file transfer system. If the only way to get a functioning product is to get a replacement or start with a clean slate, that's a joke in 2021.
That tells me that it's a software issue, but since it's hard to pinpoint/replicate and at least with some P6 Pro users even a factory reset was not able to help, you might have to get a replacement model.