Hmm, perhaps its something that changed in more recent versions then. My phone has one of the Android 12 betas on it. I certainly do remember this being a thing though, but not in a while.

At some point might you have gone to Search > Settings > General and unchecked "open web pages in the app"? Pretty sure that setting is on by default.

The Google app uses Chrome Custom Tabs, which allows the calling application to filter the browser implementation by application ID. The documentation encourages this by showing how to limit to the various Chrome app IDs (stable, beta, canary, and dev). Naturally, the user-respecting action is to try a CCT request with the default browser and fall back to known app IDs, but Google themselves don't do this and don't show how to do it in their documentation.