I cannot believe that the supposed remedy for this situation is to reinstall Windows. I just built myself a new gaming PC from scratch with a fresh clean install of Windows 11, and I had the screensaver issue. I don't use sleep, hibernate, or hybrid sleep and disable those in power options every time, so I can't comment on that.
I've built at least a couple hundred PCs since 2000, and there have been screensaver issues since Windows XP. Microsoft actually acknowledged this issue as far back as XP, and had a remedy for it within Windows Update. The problem...certain Microsoft branded mice. Mine was wireless, so I don't know if this affects wired mice too since I haven't ran into a wired MS mouse in a while. It's default driver would allow the mouse to tell the PC that the mouse was moving, so slightly that your eyes couldn't see the pointer move on the screen. There was an alternate driver back then to be used if you encountered this issue.
So the years go by and I move to W7. Same problem. I built Vista machines for customers, but never ran it on one of my own machines. This time, no solution from MS. Eventually, realizing they weren't addressing it this time, I had to abandon my favorite wireless mouse to this day, and grab a Logitech mouse. Problem solved immediately.
I chose to skip W8 too. I build a W10, no issues simply because I'm still running a Logitech mouse. Who knows if the problem still persists.
I build my new W11 gaming rig over the past few days on my bench using a generic, basic, unbranded bluetooth keyboard and mouse. Takes me a good 4 days to get all of my software tweaked the way I like, screensaver works flawlessly. I'm done and this W11 PC can now be put at my desk and replace the W10 PC. I leave my PC on for days to months without restarting. I walk into my office the next morning and the screen is on...Whaaaa? Time to troubleshoot. I set screensaver for 1 minute for testing purposes. Disconnect the Logitech mouse, nope. I disconnect the two external backup drives one at a time, nope. I disconnect the USB DAC that is my soundcard, nope. Then, duh, it comes to me. I'm using my trusty old Microsoft wireless keyboard that worked fine with W10. Pull the battery out, still no screensaver. Remove the receiver...one minute later, screensaver kicks on. I plug in the unbranded wireless receiver and keyboard, screensaver still working. Plug my MS keyboard back in, no screensaver. If you check device manager for your MS keyboard or mouse you'll see that the HID driver that installs by default is from 2006. It doesn't appear that it's something they're looking to change anytime soon. I tried various remedies such as finding a new driver or setting device not to wake and such, to no avail. No dedicated driver for my keyboard, and their software suite can't locate my device. I was just looking at backlit keyboards the other day, and this basically made my decision for me. And you can bet it won't be a MS keyboard either.
So, long story short, for some reason Microsoft can't get their own peripherals to work with their own OS. When even a cheap unbranded keyboard and mouse work, but not a nice MS set, there's a problem. Had I contacted MS, which I never bother with, and their advice had been a re-install or anything similar wiping out 4 days of work, only to have the same problem, I'd have lost it. Check those Microsoft keyboards and mice people. Hopefully this helps some of you.