Ok, sorry for the delay in getting back here, but I was very busy & this is a hard one to parse. I wish you had created your own new thread so it would get more eyes on it. I can provide you with a few possibilities.
I'm concerned about the "Unsigned Files" section which mentions the Microsoft Edge updater. I would expect all MS software to be signed.
I'm also concerned about the HP printer software which has a Kernel Extension (not loaded at the time of the EtreCheck report). That is a deprecated way of providing drivers with recent versions of macOS. Although it appears you have updated some parts of the HP software which may mean HP is just very lazy, or this is a component which is very old & has not been updated.
And another oddity is the fact that the User LaunchAgent section shows the "DropBox.app" is in the Trash. The install date is listed as 2025-05-15. So there is something odd there. I would see about updating your DropBox software since that seems a long time for such software to go without any updates or patches.
Now we come to the third party software which I am unfamiliar and don't recall ever seeing it listed in any other EtreCheck report. Odd & unusual is always a good place to start when someone is having problems.
- Emergent3 -- has a user LaunchAgent
- Prism (nchsoftware) -- also with a user LaunchAgent, but it was not loaded at the time of the EtreCheck report.
It appears this Prism app was deleted, but was not uninstalled properly since it left behind a .plist file as shown in the CleanUp section of the EtreCheck report. The left behind .plist file should be removed.
- Navigate to the hidden "~/Library/LaunchAgents" folder within your home user folder and
- delete the "com.nchsoftware.prism.schedule.LikeSurvey.plist" file.
If your screensaver is the trigger, then the MTLCompilerService which showed High CPU use may be related since that is related to the macOS graphics/video rendering.
So is your laptop still working Ok since you changed your screensaver settings? Have you tried changing the setting back to see if the issue immediately returns just to confirm that is the trigger?
Was your previous screensaver setting using random pictures you provided? It is possible one of those pictures has an issue or it may just be a compatibility issue with one (or more) of those pictures due to its exact format.
It is also odd that the EtreCheck report shows what appears to be the same MS Office update being installed on two different days. I don't know what to make of it. Just an observation.
Hopefully some other contributors will review your post & EtreCheck report, or correct me if my notes here are irrelevant since I am not a macOS software expert. This is definitely a case where more eyes would be helpful. Hopefully the problem really is with one or more of your photos that the screensaver was attempting to use.