Apps have worse ability to track you than a browser, not better.

• no possibility of using third party cookies
• no possibility to fingerprint you using what modifications your extensions do to the DOM

The only extra information they get about you is a consistent but unique (as in not possible to correlate) identifier, meaning they know its the same device accessing the app that it was the other day as well. But they often know this from IP on the web anyway, and since it can't be correlated, it doesn't tell them much.