. . . Also, with the coinbase tx, the scriptPubKey is kind of replaced by another script that handles sending the earner the BTC and this is ultimatly verified through miners working for BTC + transaction fees . . .
So close, but it still sounds like you're a bit confused on the specifics.
In a coinbase transaction, there is no "script" that replaces scriptPubKey. The coinbase transaction has no scriptSig in the inputs, but it still has a normal scriptPubKey for each and every output setting up the requirements for someone to spend that output in the future.
Nothing "handles sending the earner the BTC", BTC are never "sent" anywhere. Transactions are simply added to the blockchain.