There is no concept of "only this site" in a simple Apache virtual hosting setup, as all sites are defined in one configuration typically built from many files. There is one server process that may spawn additional processes or threads to serve requests but they each just see the whole config.

To put a configuration change into effect you can mostly do a graceful reload, which is what is happening when you do service reload apache2 or systemctl reload apache2 or apache2ctl graceful. This takes care to finish serving every outstanding request with the old server process and then hand new connections to the new server process that sees the new configuration. There will not be noticeable unavailability. I say "mostly" because there are a couple of configuration changes that do require a full restart.

You asked in comments how production services handle this, if the web server has to be restarted every time there is a configuration change. The answer is that setups which desire high availability would put load balancers in front of web servers so that there were multiple servers available to answer requests. That way a configuration change can be done by rolling reload without clients noticing.

This is done not only for configuration changes; it also helps to protect against problems with any small number of web server hosts. In your current setup you have just this one web server host: if anything happens to it, it all the sites are down.

Very popular web sites will eventually also exceed the ability of a single web server to serve them, so a load balancer is the way to scale horizontally.

The single point of failure then becomes the load balancer, so that too must be made highly available and so it goes on, with ever more complex setups.