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
In reading about the Sealed Sender protocol, as I understand, it redacts whom you’ve contacted. However, the metadata does include timestamps. I have no dog in this hunt as 99% of my messages are whispered into someone’s ear. Still, one must implicitly trust the receiver of such whispered messages. I honestly don’t care what app you use. Those choices are ultimately yours and yours alone and hopefully dependent on who you entrust with your data. This is just an interesting dissection of Signal and privacy/anonymity for the muse.
In the end, we all trust some entity whether it be your ISP who has your bank account info and residential address and can tell when you’re downloading 150 gigs of Linux distros overnight even with a VPN, a bank with every last transaction you authorize, the time/date, or government to which we pay income taxes who has pretty much all the info they would need to show up at your doorstep. If your threat model precludes all the above, I would recommend whispering and disconnecting from society. I honestly do not see any other way.