That’s a good question I’d like to know, too. Perhaps they hash the phone numbers then compare to their master list for matches?
Still, one has to possess and reveal a valid phone number to use the service. This must help to grow the user base.
It sounds like Signal is trying to solve a different problem than the one you have, so you should probably look for a different solution.
IIRC, Signal's goal is easy to use mass-market E2E encrypted replacement for SMS messaging. If they didn't automatically notify people's contacts, then most of them would probably continue to SMS or use FB messenger, etc.
This form of number is also the one your (mobile) phone actually uses, although they let you type in any sloppy human attempt at a phone number and translate.
Signal apps periodically reach out to Signal's servers to do two things: Confirm that this specific user does still have Signal (and so messages to them should be accepted) and optionally upload a set of these hashes for their contacts to see if any of those have Signal and so messages to those numbers can go securely via Signal instead.
B. You can exchange identifiers with people whom you want to communicate it just like with any other non-phone-based system: "Hey I'm @username on signal", "Cool, I'm @username2" - composes well with method A.
Solution B ties in to a bigger argument I won't address
I just don't see it as a casual thing the way the target users of these apps apparently do.
I want to explicitly control, per any form of communication, each person who is to be made to know that I operate that form of communication and whether or not that form of communication with me is open to them.
I do not want to open up a new app and have a large populated list of past acquaintances appear, I absolutely do not want to appear in such a list, I would rather not use a given app than risk having someone show up messaging me uninvited.
This is a privacy trade off. Some services chose to keep this list. Signal chose to use phone numbers.
"Hey, add me on telegram, my username is @andrewzah". This isn't a hard problem.
I don't know why we decided apps hoovering up our contact lists in exchange for convenience was so important. For an app that touts itself as private and secure, I still had to explain to my brother why giving it his contact list wasn't a good idea.
This is very different than Signal doing it automatically when I join.
the contact prepopulation isn't even that useful. telegram in particular seems to drop notifications if you don't exclude it from power management on Android. if you don't know the user has notifications turned on and has jumped through the hoops to make them actually work, you may as well send messages into a black hole. this is part of why I never assume it's a good way to contact someone without explicitly asking.
I fully understand it is just creepy, and lots of people want the option for this alone.
I'm also wondering if it is to do with notifying people you hope think your number is dead that it is very much alive (people you have ghosted).
Any other reasons? Perhaps this should not just be an option, but an opt-in one.