Really depends on where and how the data collection is integrated.

Browser forks mostly make changes to the application UI which wraps the engine, not to the engine itself. Browser engines are these fantastically complex things, extremely difficult to keep operational and secure, which is why there aren’t many of them and why they’re all developed by large organizations. Forking the engine is basically doomed to failure because you won’t be able to keep up, you’ll be out of date in a month and drastically insecure in a year.

This is basically all there is.