For example, I first sign a transaction with seed 1. Then I sign this transaction with seed 2. The transaction is valid because it is a 2 out of 3 multisig.
Then I copy the first transaction and signed it with seed 3 this time (instead of seed 2).
So now I have two signed transaction (actually this is the same transaction). Every signature is done offline on my airgapped computer.
What « happened » if I then don’t broadcast this or these two transactions over the internet ? Is it ok ?
If you are afraid that you may have privacy issues broadcasting transactions, since you need internet for this purpose, I suggest running your own node + electrum server. Then connect a wallet, like Sparrow for example, to your personal electrum server using TOR. I think you can't really do much more to avoid connecting to the internet at all. Bitcoin needs the internet.