I use one that looks like this, though this one seems slightly newer with USB 3 (?) https://www.amazon.com/Camcorder-Definition-Acquisition-Broadcasting-Amamzing/dp/B09CNQW69J/ref=mp_s_a_1_1_sspa?dchild=1&keywords=hdmi+capture+card&qid=1633015257
Yeah, should work with consoles. You want a HDMI splitter too, so you can send the image somewhere you can see it too, and not only in OBS.
Obviously not as good as something like the elgato, reviews I've seen online point at worse color representation etc, but definitely good enough until spending on more expensive equipment makes more sense.
I've also put up a large fleece blanket from IKEA with clamps on the wall for soundproofing lol. Used to have a sock over my mic before I bought a pop filter.
Was very annoying to be able to play games on GFN and Stadia without any issues at all, and stream with OBS, but whenever I tried both at the same time, everything just turned into a lag fest... Was about to give up when this solution dawned on me