It seems that the citations that are available for Re-use in the Media dialog are only those that were already inserted in it.

• open Media dialog and insert a Cite in Caption
• re-open the dialog and then you can Re-use the inserted Cite.

Also notice that ref counter in Media Caption has its own "scope" for counting - the inserted Citation will always display [1] etc upon insertion; when saved - the counter will reflect correct counting according to the page Reference list. [1] number will be displayed again if Media dialog box will be re-opened for editing.

I'm guessing this is blocked by T49344, maybe it should be merged with T62919 though? Sounds like different symptoms of the same problem to me.