If the host where the community resides is down, I can still read existing posts, and post and comment with users on my local instance.

Can you help me understand how that all works?

I'll preface this by saying I haven't read the code and it's certainly possible there are errors in my mental model, but my belief is:

1. When the community-instance is up and it gets a post from a user local to the community... It write that data to its db and asynchronously sends federated messages to instances with users that sub the community. Those instances write it to their local DB.
2. When the community-instance goes down and someone on a user-instence tries to read the post, it gets read from the local-db cached copy.
3. While the community-instance is still down and user-a on a user-instance posts or comments, again it goes into the local DB and async sends a federation message to the community-instance... the message doesn't immediately get through though.
4. While the community-instance is down, if user-b on the same user-instance browses the community, they see user-a's content from step 3 in the user-instances-db. If user-c on a different user-instance checks, they won't see user-a's content until the community-instance comes back up to process the federation messages from step 3.
5. When the community-instance comes back up, it accepts the federation messages from step 3 and updates all subscribed instances so user-a's content is viewable everywhere.

It's possible I'm mistaken about 3-5, but if you had trouble posting... my guess would be that your own user-instance was struggling and slow. But if you've rules that out maybe the update behavior when the community-instance is down works differently than I think it does. The reading in step 2 I'm quite certain about though.