I don't know how common they are anymore, as Plex has moved toward hosting their own metadata and I've never bothered using any myself, but there historically have been some number of YT metadata agents (e.g., this one) folks could add onto their Plex server and pull the metadata from YT directly. Expanding something like this to also query the Sponsorblock API seems like it wouldn't be terribly difficult.

The harder part would be getting the player to incorporate Sponsorblock to actually use that data to skip the segments. Plex, in particular, seems unlikely to ever try something like this, as their business model is moving more and more toward ad-supported streaming content rather than improving the self-hosted media server that got them popular.