Narcoleptic 2019 iMac Won't Stop Sleeping

Hello, I have a 2019 iMac that has always struck me as a bit of a lemon. When I got it, the hard drive was so blisteringly slow that I bought an external drive and made that my boot drive instead. Problem solved! Now, 5 years later, my computer falls asleep shortly after reboot. About 20-30 minutes after restart, the iMac will start falling asleep every 15 seconds. Yes, I counted. I must complete whatever task is necessary in those 15 seconds. Then, boom. Screen is dark, and it takes a while to wake it up again for another 15 seconds of work time.

Obviously this is breaking me. I closed all software to minimum, have reloaded/updated system. Done the reset thing where it beeps a few times and restarts itself. It seems like a software issue, but I can't figure it out.

Hardware seems fine. It's not the sleep setting. I can be typing or moving the mouse; it still falls asleep. Anyone else familiar with this?

Kathrine