Can the encrypted filesystem be dismounted after copier reads the password

I want to keep the SSH keys on encrypted filesystems which will be dismounted after Kopia starts the copy.

Once Kopia reads the key and creates the connection is it necessary for filesystem that holds the file to be kept available?

I’m not sure whether this is an SSH feature or not.

ssh-add (adding a key to the ssh-agent) can be told to add it with a timer, so that it expires after say, 5 minutes or so. If (as you guess and I think I agree) ssh only needs the key at early connection time, it won’t notice or care that the ssh-agent forgot about the key after 5 minutes and will keep on using the same ssh connection until the backup is done, and then it can’t (ab)use this key again.