I recovered the backup and restarted the cloned app that I had deleted before the reboot. So the problem was not the reboot but the deletion.
It works. The database is accessible even if the application is stopped. This is quite confusing for me.
Maybe a warning should be added in the doc
The problem makes a lot of sense and I made a mistake, but I think other people can do the same.
I will take some time to fix it.
Thanks for all