Startup only to shut down? iMac 2020

Hello! I have a 27 inch iMac from 2020 that I just got last week. Yesterday I noticed some peculiar behavior when I restarted the computer.

I had just finished installing some software and I restarted the computer, as it was required. I got up and let the computer restart and go to the login screen. I was finished using the computer and just left it on the login screen. The computer was across the room from me. About ten minutes later the computer went dark. I thought it went to sleep, but I tried to click on the mouse and keyboard and got no response. It was then I realized that the computer shut down completely. I got concerned and looked up the problem on the internet. I did not find my exact issue but saw that similar issues were solved by resetting the SMC. So I tried that and then I logged on to my desktop and restarted again. The same thing happened, but I also noticed before it shut down, I saw a message saying that if I was having problems signing in, to press the power button and another key (forget which one) to boot into recovery.

I contacted Apple and asked if this was normal behavior for a new model iMac (I had previously owned older models). They didn’t seem to know what I was talking about and proceeded to suggest that I reinstall Big Sur. Which I did. The issue still existed. Then they suggested that I do a fresh install of Big Sur. Before I did, I checked to make sure it wasn’t anything plugged into the computer. It wasn’t. So I did a fresh install. I have yet to see if the problem exists still as I have yet to log into my desktop and restart. But so far, no issues.

I only noticed this behavior after restarting fresh. The iMac did not shut down for me under any other circumstance. What do you think about this?