I guess you can't find it in the f-droid app, because it's hidden because of its anti-features. You have to enable in the settings of the f-droid client to show apps with anti features, than you will find it by search.
More info on the f-droid website: https://f-droid.org/hu/docs/Anti-Features/
Edit: Also to enable opening links in the f-droid app you have to go to the app info in the android settings, where you can select the links you want to open with f-droid. Then your browser should redirect links to the f-droid clients. Here is a detailed tutorial about this, it's the same workflow with f-droid: https://gadgetstouse.com/blog/2022/01/28/open-facebook-instagram-twitter-links-in-app-not-browser/