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
mailinator still works well for a lot of things.
And it really isn’t nearly as bad as you think it is. Most of those services that are locked down to that level (like signal) aren’t worth using. Hell, even reddit still doesn’t even require email. Although they pester you about it a little now.