They are overlapping areas, but they are “two completely different things”. They overlap by sharing common goals, not by being interchangeable.

They aren't interchangeable but they intersect. Completely different means they are disjoint.

it proudly advertises you as a signal user to other signal users

That sounds terrible, a private message service shouldn't advertise anything to anyone. If I subscribe to a subversive magazine, it shouldn't advertise me to other subscribers. It's a terrible invasion if they do. Signal and PGP are both comparable to subversive magazines in that regard, even if the PGP manual tried to say the opposite.

I think most of us these days recognize that the whole concept of public key directories and signature chains on PGP keys was a conceptual error in how people thought about privacy back then (they only cared about encrypting message content). We like to think we know better now, but maybe we don't.

Okay? And? In this hypothetical world where Signal offered anonymity but still tied you to your number for other practical reasons, then you’re be correct that it would be a privacy concern.

According to Wikipedia, they do record some of that info and report it to the government when required. In fact there is further disclosure to them (they might not retain or use the info, but they do receive it) every time you connect to the Signal server.

Anyway the Wikipedia article indicates they have introduced usernames as an alternative to phone numbers, so they have finally acknowledged the problem and done something about it.