>I'm asking where is the line between "mining crypto" that is banned and that is allowed.

Well specifically here, their T&C has 9.3 (https://www.hetzner.com/rechtliches/agb):

>9.3 We are also entitled to terminate the contractual relationship for good cause without notice.

>Another important reason, that can result in block or determination without notice, may be that the customer uses content, which affects the performance or the safety of the server.

So basically, "Are you being an asshole and fucking up our equipment and/or experience for other customers? Do that and GTFO." And that's it. It's not a big deal.

>You can't say that T&C ban mining crypto for proof of stake

They certainly could. They can put anything not contrary to law in the T&C they want, and they don't need any reason for it either. They can flat out forbid cryptomining period regardless of if it's proof of work or proof of stake or proof of steak or anything else. They can do it because it mostly tends to be abusive and it's too much of a PITA to sort through and "why the hell don't you just buy your own server and colo", or the can do it if they feel it's morally wrong, or whatever.

>In other words "mining" is equivalent to "computation" of any sort

It's not though, it's mining. They can discriminate by application if they like. Now as a practical matter sure, if you're doing something that causes zero issues then even if they say "no mining" you're highly unlikely to face any sort of trouble. They don't seem to be actively and zealously out to get customers, they just don't want assholes as customers. It's obviously unlikely they'd bother anybody merely doing reasonable computation. But a blanket "no mining" rule may still be worth it to them for what to point to in case of issues given the business incentives involved. And that's ok.

I mean, it seems like you're trying to be cute here and rules lawyer as if they're a computer running a program, not humans running a business. That's not the case though. Customers and Hetzner have 100% short period consensual transactional relationships in a crowded market. Neither side owes the other anything in particular outside a single billing cycle. They don't need a bright line, and indeed bright lines tend to be INCREDIBLY challenging and a bad idea when it comes to this kind of general population service limits (ie., outside of high price serious SLA ones where someone genuinely is paying for everything). It gets too complex to tailor to situations like "John Doe has been a great customer for 10+ years and needed to do this one time super heavy thing and we're going to cut him some slack" vs "Joe Blow who just joined a few months ago on a bottom barrel tier and whined at support constantly and suddenly thrashed our hardware pursuing the latest pump and dump", which businesses certainly can and do treat differently even if both parties "used the same amount of hardware resources in a given period". If it becomes a big enough deal, a judge can sort out whether something was for "good cause" or not, but it's unlikely to go to court over such chickenfeed money (nor would an abusive customer win anyway).

In short: If you want a specific SLA with bright lines and so forth, you need to negotiate a specific contract to that effect. Expect to pay for it. If you want the "sign up in 30 seconds on the website come one come all!" offer I'd pay close attention to the T&C and in particular sections like 9.3 above, which if anything is fantastically generous to the customer vs what you'd get from American companies.