The Plex deep links will automatically resume. TV shows are tricky. For that, I use the Plex integration of Home Assistant to play a random episode. It's supposed to be super powerful, but I haven't got it to work reliably yet (which is why I didn't focus on TV Shows in the blog post).

service: media_player.play_media
data:
  media_content_type: EPISODE
  media_content_id: |-
    { 
      "library_name" : "TV shows",
      "show_name": "SHOW NAME HERE",
      "shuffle": 1,
      "maxresults": 1
    }
  enqueue: replace
target:
  entity_id: media_player.plex_plex_for_apple_tv_apple_tv

And I'm wondering if these could be adjusted to have the card be "inserted" and turn off when the card is removed?

I have some nfc tags sitting around but they are much thicker. Maybe I can 3d print something those tags can click into and make like a mini vhs player for them