When killing an emacsclient terminal via C-x C-c, it should prompt to 
save the files initially passed to emacsclient. To see this in action:

   $ emacs -Q --daemon
   $ emacsclient -a "" -c foo.txt
   $ emacsclient -a "" -c bar.txt

   ;; In the first client frame:
   foobar ;; Insert some text
   C-x C-c
   ;; Emacs prompts "Save file /path/to/foo.txt?..."

Now try the above, but call `(server-stop-automatically 'delete-frame)' 
first (or replace `delete-frame' with `kill-terminal'; it doesn't 
matter). In this case, Emacs doesn't prompt to save the file. However, 
the docstring/comments in `server-save-buffers-kill-terminal' say that 
it should: "Offer to save each buffer, then kill the current client. ... 
Only files from emacsclient file list."

Attached is a patch to restore this behavior when stopping the server 
automatically. This puts all of the logic into 
`server-save-buffers-kill-terminal', which allows 
`server-stop-automatically--handle-delete-frame' to be simpler. I've 
also added some more detailed comments explaining the logic here, since 
there are some pretty subtle aspects to it.

There's a further subtlety that I should probably mention here though: 
when killing a nowait frame, it would kill Emacs entirely if that were 
the last frame (even in Emacs 28, and probably earlier). The only way 
(that I can think of) that this could come up would be to run:

   $ emacs -Q --eval '(start-server)'
   $ emacsclient -n
   C-x 5 0 ;; in the non-client frame
   C-x C-c ;; in the emacsclient frame

However, when doing this with a regular (non-nowait) client, the last 
step would report the error "Attempt to delete the sole visible or 
iconified frame". Even more oddly, it would work the *second* time you 
tried to kill the client terminal, since `server-delete-client' would 
set the `client' frame-parameter to nil before deleting it; on the 
second attempt, Emacs thinks the frame is a non-client frame (even 
though it is).

I've fixed this in the second patch by following the nowait behavior: if 
you kill a client and *all* the existing frames belong to that client, 
it kills Emacs entirely. I'm not sure this will come up often in 
practice, but it's a fairly simple change.

Some tests would be nice to prevent this from regressing, but I'm not 
sure how to write a test that starts up a daemon and connects clients to 
it...