So basically I'm running an online game site whereby each "match" would be a certain duration, after said duration the "match" would change in name and details. How do I implement a live countdown which synchronizes with all users, which continues running on the server side even when a user closes the window?
You don't need a distributed counter for this. The timestamp you need is state, and state should be managed by the game server.
In Firebase (or Firestore) you can implement this functionality with a snapshot listener. Each client would then subscribe to this listener. See this question for an example: How to implement a distributed countdown timer in Firebase.
Also, you might find useful this thread on Reddit. https://www.reddit.com/r/Firebase/comments/mnitde/making_a_timer_for_a_tabletop_game_in_firebase/