By providing Signal with any phone number at which you can receive an SMS or text message, you can register a Signal account at that other phone number. For example, you can create a pseudonymous Google account, register a Google Voice VoIP number, and use that as your Signal number. Or you can even use a free throw-away SMS account and use that number when you sign up for your Signal account instead of your real phone number. The Signal service will happily send the throw-away number a text message with the verification code, letting you complete the account sign-up process.

Registration also works for numbers that can receive calls but not SMS. Like any landline you (even temporarily) have access to.

Does that work if some else has used that phone number to register an account already?

Not if you enable PIN locking (and the account is active).

https://support.signal.org/hc/en-us/articles/360007059792-Si...

Orrrrr Signal could just fix their shit. Requiring phone numbers for this long is borderline suspicious.

Not yet, no.

Telegram allows you to register without a phone number, as of recently.