Cheap HDMI "Capture Card"

Like a lot of people, I've spent the last 3 months doing a lot of video calls/presentations/meetings etc. I'm quite lucky that I have a decent setup already (including a HD webcam, a Logitech C920)...however I've found that running OBS alongside multiple apps can give my laptop a hard time. What I'd like to do is run a second machine (I have a spare laptop), and then use that for the video compositing/output, and use my main laptop for doing actual work.