I didn’t even know there were still cases bundled with power supplies! But yes, in general, throughout the history of PC building, I’m pretty sure included power supplies in any brand tend to be very low wattage. The power supply probably isn’t even broken - I’m just guessing the PC’s was upgraded to an RX 580, and the RX 580 was more power hungry than the original graphics card and the power supply just wasn’t designed for it.
Just a tip - next time you build or upgrade a PC, use this tool to estimate what power supply you need; https://www.newegg.com/tools/power-supply-calculator
You can get a 700 watt PSU that should work in the $50-70 range, although honestly, it might be worth it to go a bit bigger so you can cannibalize it for a future build when the time comes - even the RX 580, which is newer than your CPU, is getting a bit old and I hope to replace it if I build a new PC in 2028.

Luckily, I can probably live with using mine a few more years. Mine's an early AM4 system with a Ryzen 5 2600 in it. My CPU performance isn't a huge bottleneck (although I'd like a couple more cores for faster compilation).
Really, it's my graphics card. The 580's fine for some basic gaming, but it sort of got left in the dust with ROCm support - it's kind-of-sort-of supported, but not well enough for Blender to work with it.
I think the situation's improved with ROCm on consumer GPUs enough now that so long as I buy a newer card, I should be fine. Debian support's improved a lot as well - for many GPUs, it should just be a matter of
sudo apt install hipccnow. However, Debian is still a few versions behind in experimental and doesn't support the latest AMD cards, but I suspect that getting it packaged was the hard part, and that once Trixie releases, Forky/Testing will catch up in a few months.