In the past, I've thought of installing Signal, but never did because it identifies you by your phone number, which seems like a totally unjustifiable and idiotic idea. I'd like to keep using my internet-based service even if I switch phones. There is no reason for my phone number to be known to Signal at any point.

Just now, I tried to install Signal and WhatsApp for work communication. Neither is willing to let me do anything unless I grant them permission to read my contacts.

I use WeChat. (Not for security reasons, obviously.) Somehow, despite the fact that WeChat is heavily coupled to your phone, they've realized that it makes more sense to use a WeChat account than a phone number, and that it makes no sense to prohibit users from just adding contacts manually. Adding contacts manually is actually a preferred approach! (In the form "scan QR code".)