Getting a better video card to play Doom Eternal

I want to try to get into gaming and Doom Eternal looks really fun. The only problem is, I currently have this computer: https://support.hp.com/us-en/document/c06044144, and an HP Envy 795c, so the power supply is 310W. After my divorce in 2018, the purpose wasn't for gaming, now I'm trying my hand at it. The video card it currently has is an AMD Radeon RX 550. In my research, I can see that AMD is probably the way to go for Linux gaming. I'm currently running the latest version of Linux Mint, 21.1, Cinnamon desktop.

So it appears what I need is a list of AMD graphics cards that don't require a power supply connection (externally powered) that perform decently and I'd rather not spend more than $250 or so.

In my research, this was helpful, " The best GPU without a 6 or 8-pin power connector is the Radeon RX 6500xt. The best single slot/low profile is the RX 6400. You might also want to look for an i5 to slot in that motherboard, by the way, dual cores are gonna mess up your day regardless."For here: Best GPU without power pin? - Graphics Cards - Linus Tech Tips

Also, this is a good list I found of the performance ranking for AMD GPU cards: https://technical.city/en/video/amd-rating

I have three monitors, I need to make sure it has three ports, as well. This is just to get by. If I really end up liking the gaming experience, I will of course upgrade to a newer PC with a better power supply and video card, etc. I mean, I wish I could get an RX 6600 or something, but it requires a 500W power supply. Any thoughts? Any lists of unpowered AMD video/graphics cards?