I’m running that exact card in my daughters NAS. It’s running Jellyfin rather than Plex but I just confirmed that while playing/transcoding, I can run intel_gpu_top without issue.
Without testing it on a fresh install, it’s tough to rule out software/driver issue but my gut says you got a bad card.
BTW, it’s a great card for this use case with the one down side being the horrible fan control in the vbios. That damn thing endlessly ramps up and down. I did flash this card to the latest vbios and it helped SOME but not fully. Hopefully there will be fan control available in Linux soon so resolve that.