@Pete thanks for adding the additional infos. from the process tree it can be seen that ssh is running, that’s what I wanted to verify 
the timeout definitely suggests it’s a network connection issue. if you would suspect your own server aka iptables to be the blocker you could temporarily add allowance for ports 0-65536 TCP and UDP to override the default DROP policy. that could help if you changed your ssh port but somehow forgot about it
@Wibol suggestion is also good if you had troubles with your root access (lost key or password forgotten) - but as you said yourself are you do not even get there for now.
indeed it sounds like there is something in the way on providers side, maybe some messed up setting in their firewall/anti-ddos appliance or whatever they might have in between. best of luck that they will be able to solve it quickly.
and by the way: you should never be afraid to press that big red restart button. services you run on any server should be reboot proof. while great uptime and such might be a thing, I’d rather accept a few minutes downtime for a reboot every now and then but be sure in case it happens without my doing, everything gets back up properly by itself