I would like to create a first person shooter, but it is necessary for me to be able to search for free game servers or start them if necessary so that I would like to know how it works
This would take a lot of work, but if you're willing to take the time, you could update your own website from roblox, and take the text from said website to change the lobby server. This isn't a simple answer but it is the only one I can think of. You can read about how to do something like this here:
https://wiki.roblox.com/index.php?title=User:Seranok/Using_HttpService
Sadly, I have no knowledge on making a website, but if you could learn that then you could make this happen.
roblox automatically tries to find a slot and makes you connect to a free one