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
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.