Said differently, if I authorize a spend transaction using my hardware wallet (I am one of the four), how does the exchange (Coinbase, or any other non-Electrum) know that a second signature is required?
Thanks.
That’s the thing, you can’t fully authorize a transaction without the other parties to the signature having to sign with their keys. Their keys authenticates your transaction else, it all stays put. Coinbase or which ever exchange you might be sending your coins to don’t need to know this, it ain’t about them. It’s just you, your wallet and the blockchain network but, every initiation and broadcasting of your transaction and broadcasting is done from your wallet. Exchangers just receive it and from there, you could sell or trade as you please.