Each recording in one's listen history could have a context menu item that will copy a short stable link to a page to the clipbord

When clicked this link could work like song.link where the receiver of the link can choose their preferred streaming service:

https://song.link/s/1S3QJc8kcnHyYyIcfeNleO

The page could also provide some interesting metadata or an embedded player but the focus should be on links.

MBS-13444 could be a related feature.