Most likely someone at the AI company would catch it and filter those strings out of the training data.

Librewolf is a fork of Firefox.

From their site:

LibreWolf also aims to remove all the telemetry, data collection and annoyances, as well as disabling anti-freedom features like DRM.

In the future, Ladybird or a browser built on top of Servo might be alternatives, but both projects are pretty far from being usable right now.