Strategy for handling stateful applications in clusters

I have an application in which users are assigned to rooms. These rooms are saved on the server side. At first, I used a single instance so that parts could be saved in memory.

But now that I want to evolve, it is not a viable solution. The use of databases seems to be a very slow option, because the entries are too numerous and too fast to manage.

I've looked at memcached, but I've read that it's not reliable in a shared cloud environment (if the table is full, the rewrite values ​​start).

How can I handle such a situation?