The trace you don't see
Every time you install an app from an official store, a permanent record is created in your account. It doesn't matter if you delete it later. The store knows you installed it, on what date and on what device. Anyone with access to your family account can see it.
And that's just the surface. Most messaging apps store your conversations on servers. They make backups in the cloud. They log who you talk to, at what time and how often. Messages may be encrypted, but metadata — who talks to whom — is not.
What "no trace" really means
Talking without a trace doesn't mean deleting messages afterwards. It means no record that the conversation ever existed. Not on a server, not in a cloud backup, not in your app store purchase history. That requires three things.
First: messages must not pass through any server. If they do, someone can store them, analyse them or hand them over if asked. The only way to avoid this is for them to go directly from one device to another.
Second: the app must not be downloaded from any store. If you download it from a store, it stays in your purchase history forever. The alternative is a web app that installs from the browser — it works just like a native app, but leaves no record in any external account.
Third: you must not need a phone number or email to register. If you register with your number, you're already linked to your real identity. If you register with an email, there's a trail. Privacy starts with being able to create an account without giving away personal data.
Three things you can check yourself
You don't need to be technical to verify if an app is truly private. Open your browser's developer tools and check three things: are there cookies? Do requests go only to the app's domain or also to external services? Is data stored in any cloud?
If the app installs cookies, someone is tracking you. If requests go to third-party domains, someone is receiving information about you. If there's an automatic cloud backup, your messages are on a server you don't control.
The right question
The question isn't "does this app encrypt messages?". Almost all of them do. The right question is: "where is my data when I'm not looking?". If the answer is "on your device and nowhere else", then you have real privacy. If the answer is "on our servers, but encrypted", then you have a promise. And promises can be broken. Because a server, in the end, is just someone else's hard drive. And that someone is not you.
There are apps where your data only exists on your device. Where messages go directly from one phone to another. Where you don't need to give your number or download anything from any store. Where the only person who knows you use them is you. They exist. You just have to know where to look.