The reason I ask is because I've been considering providing MongoDB hosting on our own servers so people don't have to use remote databases. It seems to be a pretty popular database system, but I haven't used it at all myself. I suspect it would be a fairly sought after feature if we were able to start supporting it. Installing it and maintaining it would definitely be a learning experience for me and I love learning new things, especially stuff related to hosting and computers in general.
As far as getting logged out, if it happens in less than a minute or so it's probably because your IP address is changing. Plesk hates it when your IP changes and it logs you out, sometimes only after a few seconds. If you get logged out after 30 minutes or so, then that's just by Plesk's design. If you install PhpMyAdmin or Adminer in your httpdocs folder you can set the logout timer to whatever you want. For example, https://stackoverflow.com/a/64480479 https://stackoverflow.com/a/11858297