Yeah, post a screenshot of task manager running while Oblivion is running. See if the game is bugged and overtaxing your system or if it's something else.
HDD is terrible for gaming, especially on games like Rust and Battlefield. Also, AMD usually suffers from a few optimization issues.
Sounds stupid, but have you made sure that those games aren't using the integrated graphics on the motherboard?
You can try these:
https://www.tenforums.com/performance-maintenance/17899-monitor-turns-off-after-2-minutes-inactivity-3.html#post441903
https://www.dell.com/community/Laptops-General-Read-Only/XPS15-laptop-randomly-hibernates/m-p/5113392/highlight/true#M916473
You'd be amazed at what can actually power most games. Don't forget that some gaming PCs can cost $2,000+ and play everything at max, while a $300 console can run the same games with lower FPS and image quality.
If you're ok at medium settings and 30 FPS, you can probably run 90%+ of games on...