A lot of the latest AAA games will only allow you to play multiplayer if your account ALSO has a verified phone number attached, and they only let you attach each number to a single account, plus they filter out phones which are not postpaid (so no using services like Twilio).
No. Overwatch 2 did this and rolled it back pretty much immediately. CS:GO and DOTA2 don't require it but it they gate competitive play behind it. That's not a lot of AAA games.
Is there some way they can check with the provider for a given number? Seems less than ideal from a privacy perspective.
Some people found themselves that they could no longer play the Overwatch franchise after having bought the $40 original game because of this. This was later rolled back and they allowed prepaid phones. So they can definitely distinguish them.