Hetzner just like every major other server/cloud rental out their does prohibit crypto related activities in their products. This is not limited to "mining".
They do not need to access you disk to determine that. They can just observe behavioural patterns and use heuristics.
E.g. 24/7 100% cpu, low data, port traffic on typical crypto related protocols to known crypto endpoints will raise red flags.
They can terminate you for any or no reason with 30 days notice, and terminate service immediately for suspected abuse or non compliance.
Seems this already happened twice to you. You can try any non specialized cloud or server renting provider, and the result will be the same.
The type of server, dedicated vs shared, very much does matter. If you grab a shared resource for 100%, you deny all other shared users their usage opportunity. Bursting upto 100% occasionally is very different from 100% sustained. You know this very well, and you are reasoning from a bad faith pov. Using a shared resource 100% by definition makes it not shared.