Nowadays, a majority of apps require you to sign up with your email or even worse your phone number. If you have a phone number attached to your name, meaning you went to a cell service/phone provider, and you gave them your ID, then no matter what app you use, no matter how private it says it is, it is not private. There is NO exception to this. Your identity is instantly tied to that account.
Signal is not private. I recommend Simplex or another peer to peer onion messaging app. They don’t require email or phone number. So as long as you protect your IP you are anonymous
If Signal isn’t private, then why it is recommended over WhatsApp, Matrix and over SimpleX?
OP is confusing privacy with anonymity.
I’d say the two are different but related.
Seems OP is discussing the loss of anonymity, but the below ARE privacy concerns:
Granted that it is difficult to completely obfuscate some aspects of your identity.
Those two concerns has been fixed last year.

Because it has become extremely popular, that’s just how it goes. At one point, even Telegram was recommended for being super secure or private, but the privacy is mild on Telegram at best.
But by comparison to Instagram or Whatsapp, it’s how the gram looks like Privacy Central, so it was recommended. Now, Signal is replacing that role.
Signal is more private than the sus apps like IG, Facebook, etc. Yes. But only because those apps are so bad.
No one should be recommending signal over matrix and simplex. It’s probably more secure than whatsapp, but both have social network graphs of everyone you talked to, and when.
Matrix’s encryption algorithm was broken for a while and when it was fixed it it took app devs years to migrate to the new requirements. It still might even be the case for a lot of them, I haven’t looked in a while.
SimpleX should be secure AFAIK though, but I’ve heard that it may not be able to scale well to larger user bases. It seems everything has pros and cons.
Because most people don’t consider the very basic concept made by op.