You almost got it right, good enough this time, but next time, follow the whole instruction. Input/output means to include the command that generated the output, so that it's clear what you pasted.
You laptop's GPU shares system RAM, so it's possible you have failing RAM. Running memtest86 or memtest86+ several hours might confirm or deny this is an issue. If your laptop has more than one installed RAM stick, you might wish to try removing half the RAM to see if this has any effect, then switch to having only the other half installed if no effect.
This also could be a software issue. Your LightDM login screen should offer you an option to try some session type other than Cinnamon. If it does, try it to see if the problem persists. It may offer IceWM, which is rather simple, and if there is no option beside Cinnamon, it's a good lightweight one to install for testing.
https://wiki.archlinux.org/title/Intel_graphics has troubleshooting information you could try. All my Intel GPUs are newer or older than your Ivy Bridge, so I'm not familiar with anything specific to it. i915.enable_psr=0 from there is what I think I might try first. At your Grub menu, strike the E key, navigate to the end of the linu line, and append it after a space before proceeding with boot to test whether or not it helps.
It's possible there could be a clue to the problem in the file Xorg.0.log present in either /var/log/ or in ~/.local/share/xorg/. Share it thus:
Code:
fpaste -x 86400 /var/log/Xorg.0.log
to upload it, then paste here the resulting URL. If doing so presents a problem, try renaming it to Xorg.0.txt and attaching it to your reply, but don't try to paste the whole file. It's too big.
You're not fully up to date, so try getting there too. Latest Fedora 36 kernel I've seen is 6.2.12.