Seems fine, in the end I had nothing to do
I'm relieved it wasn't a system/disk crash, as the last backup was from Tuesday and I didn't have a lot of extra time currently to reinstall everything.

If you notice anything unusual do not hesitate to report it.

Actually the web works, but seems very slow. I guess it will improve in the next minutes/hours: after reboot nothing is in cache and it has to write lots of things in log files it seems.

Server has been rebooted. I can connect again to it, but the public web part seems still not available... investigating

The server seems unreachable.
I got an e-mail from the hosting company notifying me that there is a problem and that there is an intervention on it.
I do not have more information for the moment.