The Skylake-tier quad-core is enough of a PC for most people. Even the iGPU is fine for old games. You can build a credible gaming PC for around $200 with an old office PC, cheap used GPU, maybe extra DDR4/storage. Low profile options are generally bad or expensive, so you might want to find something that can fit full height.
Even older junk is still usable:
https://www.youtube.com/@BudgetBuildsOfficial/videos
We've had the tariff scare, the RAMageddon, now Iran scare, and possibly the long-anticipated Taiwan invasion 2K27. Get what you need, keep an eye open for deals, and settle in.