It’s a live album so it doesn’t make sense to repeat live version on each track.
See the physical edition back tracklist, it certainly does not show live version on each track:
It’s something that eShops do, probably because they don’t have a disambiguation comment that would be needed to be able to show these recordings as live on their own page (outside the release page).
You can, actually you should, use the recording disambiguation comment to store live info, and relationships.
You can make recording comments visible in release pages if you use the INLINE STUFF userscript.
I think this feature should be added to MBS, without requiring a userscript, BTW.