for the sake of proper database design and normalization, should I setup a foreign key relationship between Post and Media?
For "proper normalization" you have to assure that there are no "update anomalies".
If someone updates a Post, what happens to Attachments and Media? Will renaming a post disconnect the attachments and/or the media? If so then your FK is wrong. [Hint, you must use surrogate keys not the name of the post to make your FK's work.]
If someone wants to "move" an Attachment from one Post to another [i.e., update the Attachment's FK reference], what happens to the Media? Does it stay with the Attachment and move to the new Post?
Could you wind up with Post having Attachments and Media, as well as Attachments having Media? Could the Post and the Attachments disagree about the Media because the Attachment was "moved" but the Post wasn't also updated?
If you can have contradictions, you have broken 2nd Normal Form and you have repeated key relationships you should not have repeated.
Proper Normalization is easy.
Data Depends on the Key and Nothing But the Key.
Do not copy or repeat dependencies anywhere. What you're calling "deep linking" appears to be a repetition of dependencies.