Will 2 sets of Airpods interfere with each other?

When my roommate and I had the same kind of generic earbuds, one paired to my phone and the other paired to their phone, they would often cross over to the other one. If they were listening to something, my earbuds would unpair from my phone and suddenly I'd be listening to whatever they were listening to, and vice-versa. There was no way to undo this once it happened, we both had to reset everything and start from scratch.

Will this happen with 2 sets of Airpods (Pro 3)?

The way I understand it, when you pair bluetooth devices, you have to to give permission from both devices, usually with a code number they generate that matches on both ends. So I don't know how the generic earbuds could even have done this. We never found a solution for it.

Now, with expensive iPhones and Airpods, I definitely don't want this to be happening. And if it does, is there a fix?

I appreciate any information you might have.

Thank you.