I happen to have that exact same adapter. It can provide FullHD, but only at 30 fps. At 720p it manages 60 fps fine.
I suspect this happens because it doesn't actually have enough internal RAM to buffer a full 1080p frame (this chip uses on-die RAM, so probably SRAM since they wouldn't go for a fancy EDRAM process, and SRAM is expensive by capacity).
https://www.naut.ca/blog/2020/07/09/cheap-hdmi-capture-card-...
Take a 4k video, encode it into 320p, then encode that into 1080p. For the matter of what they are discussing, your video file will be true 1080p. For the matter of what you are discussing, that video will be horribly blurry and full of artifacts.