No, HDR has nothing to do with 10 bit, 8 bit can also be HDR, in both files and in displays, Nvidia/Windows supports that.
HDR is PQ or HLG transfer and those transfers are HDR.
H.264 supports even 14 bit. That is not a problem.
You should see that PQ transfer the file tagged with in Mediainfo. That means HDR is in use. Same about AVIF images.