Not quite. With a phone number a random phone provider knows your identity. They do not get notified you are signing up for Signals. Google doesn't know you signed up with that phone number for Signals either. Depending on your country and how these details are handled there may not be an easy way to lookup who you are from a phone number.

There's obvious downsides to the phone number use, of course, but saying it the same in terms of privacy than this, doesn't feel correct.