This capture card works well under Linux, as tested on Debian 12 (X11, haven't tried under Wayland but it should work). This device is expected to work quite universally as its a UVC compliant device. You always want to look for UVC compliant capture card to ensure compatibility. But don't blindly look for UVC devices either - there may be also other factors at play with some cards - so always read the reviews. But this one works.
There is one odd quirk with this Elgato device which has been reported by Windows users also from what I can tell; quite often the output image to a monitor (not captured image though) has a very strong green or magenta tint, which is not acceptable for any session, and the solution is to keep reconnecting the USB power cable or the HDMI cables until finally the image will display normally. It always becomes normal after a few tries. Still, irritating. Interestingly, when my Debian is capturing a Windows machine, there's never these issues. Only when I'm capturing the recording device itself or Android phone.
You might also want to ensure the device is on a stable platform and won't shake as the connection might get disrupted. You'll probably have a half-way faulty HDMI cable if that happens, though. The Elgato will come with one sturdy-looking HDMI cable. For the optional HDMI out, you'll need to buy a separate cable if you don't have one.
You might be wondering how this device works. It's rarely explained anywhere. The device has 3 ports; one for USB power, which you connect to your capturing computer. Next is HDMI in, which goes to the device from which you will capture video. Next is HDMI out, which is to optionally get the captured image to a monitor of your choice. If you are going to capture video games from a PC, you will need two computers, period. Even for most retro games. Otherwise you'll have dropped frames. Why? Capturing is a heavy task. Most computers, even high-end ones, will not be able to handle gaming and capturing on the same machine, even if you have this capture card. (Perhaps you might have success if you have two graphics cards on one computer and are able to utilize one for each task somehow?) It won't move the stress from your computer to the capture card in any way. It is designed for allowing you to connect external devices to capture from.
Recording works great in OBS Studio. Ensure ALL your resolution settings everywhere in OBS match the resolution you're capturing for best results.
I would give 5 stars if I didn't need to fidget to get rid of the tint sometimes. But note that it doesn't affect the recording quality in any way. It could be that a firmware update might help. Recommended!