I think it shows your name and profile picture, but not your phone number.

Correct; it’s actually best to think of the name field as “displayname”. If that’s not what you want you can change it.

Interestingly, it also doesn’t reveal your username, and allows you to change usernames without losing already existing chats. So a trick I’ve used is to change my username to something random, give it to someone in order to establish a conversation then change my username back. Now I have a conversation where neither of us can see the phone # or username of the other.

I think if they have your phone number in their contacts, Signal will add that to the Signal contact, and so someone can find your phone number by adding every phone number to their contacts

Yes, but I handle this by not allowing signal to access my contacts. It’s worth checking out your various ai and assistant settings on your phone as well but that’s a bit of another topic.

Edit: I just realized in the final paragraph the concern was other people finding out you were on signal by them giving signal access to their contact book. As I understand it, if you were trying to hide that you have a signal account from people who would have your phone number this would be genuine concern. Personally I don’t use my primary phone number for signal which makes this a non-issue. If you don’t want your normal contacts knowing you use signal then you should get a second number and register signal to it instead.