I don’t know of any HDR streams that use Mpeg 2 to compress as it’s an 8 bit codec and was used with DVD and in content delivery for broadcasting. I assume you mean as a transport stream? For streaming HDR content for DV or HDR10 it needs to be a minimum 10bits to preserve the ranges needed to display in wide gamut. MPEG -H 2 part 2, h265/ HEVC is commonly used for this which is a variety of mpeg encoding that is far more efficient than mpeg2 or h264 for the lower bitrates, but larger resolution needed and maintains the required bitdepths. Yes its still lossy and using 4:2:0 colour encoding as opposed to 4:2:2 or 4:4:4 will result in some loss of colour accuracy , but then all video content has to be or it would be of no use to anybody to stream lossless.
They both use the same compression schemes but I guess the DV metadata can be used to negate some of these effects as the content type is known to the encoder as it’s created, but this data is still gone in either format. DV likely can just hide it better. Saying that I am yet to see any h265 content in hdr10 that has shown artefacts common to h264 or mpeg2 as it really is a significant leap in encoding.
But if the mastering is bad no tech really will save it, and at the moment the industry is in a big learning curve for this in all sectors. Like hires audio we have a lot of faked HDR content out there to that’s been upscaled. Disney just been caught out on this with some of their content.