I have a G915 and three of my friends do - all have had problems with them (at least one nonfunctioning key and other issues). whereas the older trusty g613 is still going strong. newer logitech hardware is off the list which is a shame - unless they turn it around.
Not really a gnome person myself. Maybe you should consider installing KDE onto the systems like everyone has suggested in the comments. Don't worry you can have more than one Desktop Environment on the PC at login you can then choose under the options button which DE you want to log in on...
another option to see if it is a configuration issue or hardware issue would to be load on a linux distro to a USB live environment (running live off the usb - not installed on the system) that has the nvidia proprietary drivers pre-installed and then run a game (just make sure you choose one...
I had this happen on a Windows (work) laptop recently (not the same model) - down to 400mhz mega slow- the solution was to unplug it and replug it.
Could be worth a go before you go down rabbit holes. Best of luck.
Sorry to be the one to say it - but maybe you should consider dual booting into a Linux distro. If you've got the storage space no harm in trying - most of the games you listed I'm pretty sure run.
Force the resolution and hz through the OS and make sure that ultra hd deep color is set on the TV settings for the particular HDMI port you are using (not sure if this is needed in c4 model but it is in the older models). I'd suggest also having the TV in game mode.
Yes I would upgrade the cpu - at a minimum a 5600 - if you can save a bit more the 5700x3d - that will then last you much longer. It will make a lot of difference vs a 1600. - note that you will need the bios updated otherwise 5000 series won't work.
I mean it's a self imposed arbitrary release date long term support ubuntu users can wait and if they can't then they should probably consider an arch based option or ubuntu 24.10.
https://itsfoss.com/switch-kernels-arch-linux/ - is a pretty good website with useful well explained articles for questions users may have.
add the 'lts' kernel - you can add multiple if you like - i have the regular arch, lts and zen kernel for example. switch between them no worries.
fallback...
Looks like it could be some hardware starting to fail. but I think I read somewhere theres some issues with the 6.12 kernel and nvidia 565.77 driver? have you got another kernel version you can load into and try it out?
how about a deep dive into the terms and conditions of use- to see what users are allowing nvidia access to on their pc? maybe that will explain some of the performance.
I would recommend getting a USB and installing Ventoy then downloading a few distros with a live environment, that way you can test the functionality of the laptop - test the function keys etc. Eg Mint, Ubuntu, Kubuntu, PopOS etc
I don't have oracle and not sure what you are exactly trying to do, but if it is just for managing applications on startup - you could see if there is an app called 'startup applications' - it exists in Pop!_OS 22.04 which uses modified gnome. I'm not sure if the version of gnome that oracle...