Newbie learning about multi sig. I watched a number of videos on how to set up multi sig using Electrum and various hardware wallets. I understand the mechanical steps one would go thru to set up multi sig. But something fundamental is not clear to me.

Let's say I set up a "2 of 4" scenario, where two of four individuals (via their hardware wallets) must sign a bitcoin transaction. Where is this "you must have two of these four" rule stored? Is it somewhere on the bitcoin blockchain?

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.