Interesting, I always thought socket activation meant defer launching a process until somebody tries to access it through the network, but... does it also finish the web server process (or whatever is used here) as well after the request is serviced?
No, it doesn't automatically close the process. Two options I can think of: Application exit when it's done with its thing or RuntimeMaxSec to make it close after a while.
systemd passes the socket on to the application so I don't think it has any reference to it anymore, so it wouldn't be able to know when the socket closes.