This article explains how to create a second phone number, for usage for Signal. Which confirms my assertion that you need phone number, and makes your statement of "no" completely false. Among options offered:

The desk phone at your office.

A free Google Voice phone number, if you live in the United States (this is what I do).

Any phone number from any online calling service, like Skype.

A cheap pre-paid SIM card for a few dollars a month (and temporarily put it on your phone to register your second Signal number).

Twilio, a cloud service that allows developers to write software that makes and receives phone calls and SMS messages.

Obviously, each of those still requires registration within government-controlled phone network, and additionally also may require you to entrust your security to a third party - such as your employer, Google, Microsoft or Twilio. So in fact, you refutation of my assertion "you need to publish a phone number" is "you can have two phone numbers". This is not serious.