I have a firefox recovery key that i made on my desktop computer which is now not accessible. So I turned on my laptop but i forgot my firefox password that i made on the desktop i however did have my recovery key that i created when i was signed into firefox on the desktop, so i clicked reset password it sent me a reset password link to my email but it did not ask me for the recovery key, when you create a recovery key does that key only work on the firefox your signed in on that computer only?

Like can my recovery key only work on one device signed into firefox and no other? no other computer will the recovery key work?