Ole, thanks for the idea, but I think you over looked some details in your plan.
Relative links aside, what you are suggesting will actually serve to deanonymize you, and is worse than accessing the service over tor. With tor, your connection would be like so:
you → tor guard node → tor middle node → tor exit node → tutanota server
But you are suggesting the following flow:
you → tor client guard → tor client middle → tor client exit → tor onion exit → tor onion middle → tor onion guard → your server → tutanota server
The only advantages you would see are if you and your server come from different locations, you do not trust the ISP/nation-state you are connecting to, but are fine giving up anonymity between your server and tutanota, because your server will connect directly to tutanota.
As a general rule hidden services are most practical when run on the same host (or internal network for load-balanced servers) as the server that hosts the content.