But internal local servers which operate essentially like external hard drives, not cloud or internet servers.
If there is a need to share files over the internet, customarily VPN with FTP is used in a closed server environment. This is much different than using public access internet or cloud services. There are IT staff that run things and ensure operation and a very limited number of users, even if that number is in the double or triple digits (it's not in the millions).
There's no "super secret" method in play, just the same methods anyone would use but scaled to meet demand.
Controlling access is more about workflow management than any automation. There are workflow procedures in place to control multiple individuals working on the same thing at the same time. However, common files, such as logos/photos, would be available to everyone at all times.
Even Adobe highly recommends saving files locally, working on them, then uploading to the server again. So, traditionally you would merely mark the server file as being edited, work locally, then replace the server file when done.