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Have a look at piku (https://github.com/piku). I built it especially for that kind of thing.

The web-app integration is completely optional and you can disable it for each app individually.

E.g. your database can be an app that doesn't have any web frontend.

You could probably use something like this or dokku? They don't only host web based apps.

Caprover can run non-web too, from databases to apps