Antique Italian table, needs repair (Ashburn, VA)

This antique wooden table is in pieces. It comes apart and fits back together without nails, but it does need glue in the joints to keep them together. It can convert from full to have width but the little piece of wood that does that is broken. I hate to trash it because the top alone is so pretty. Maybe you know what to do with it?

The first screenshot is a google search result of me looking for a similar table.

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