Did we prove with a STARK proof the execution of the First ever transaction from Satoshi to Hal Finney ?

Yes absolutely.

In less than 2 months, we implemented the Bitcoin Script VM in Cairo. (check code: https://github.com/keep-starknet-strange/shinigami)

Another showcase on how powerful it is to have a specialised high level DSL optimised for ZK.

Proving integrity of arbitrary computation is extremely powerful, and it can benefit widely to the Bitcoin ecosystem, and the good news: even without any soft fork!

Yes, there are use cases and things than can be improved using STARK proofs, completely offchain.

Stay tuned, it's only the start!