Setting up Thunderbird
 

I'm in transition to a new hosting service....using the established methods, I have no trouble with email basic setup.
The question:
Using IMAP for incoming, should I expect that folders and whatnot will stay synced?

Related: If I bring in the right files from an earlier setup, will folders (or anything else) get re-synced?

More generally, I have always believed that IMAP was intended to keep the server-side and client-side files in sync.

Keeping the client side in sync is done by the client. Some clients (iOS mail is one) sync to the server every time they’re started.

I use IMAP and Thunderbird and have no issues. My iOS devices and laptop (main driver) all stay synced really well.