Most web servers support greaceful restarts, i.e. reloading code and configuration without downtime. Usually you just send a pre-specified and documented signal to the process to do it.

For a web server serving from the filesystem, sure. That doesn't help you deploy a new version of a web application you're making code changes to (which is the kind of thing that would need a database).

I was actually talking about both. For example for python, which is what I usually use, both uwsgi and gunicorn support graceful restarts. Admittedly I don't have much experience with other languages, but it's technically possible. If your application doesn't support it out of the box, you can still achieve it with something like systemd's socket activation.