Okay, it worked as I needed it to. useContext must still be instantiated, direct access via the vanilla client would be even better, but it works via useContext(). Here is how to use it according to the docs:
First instantiating mutate from useMutation every time seems to be quite inconvenient.
I'm refering to this part of the docs https://trpc.io/docs/quickstart#querying--mutating. I'd like to call query and mutate like described: