Test plan

1. Open Brave and visit brave://settings/search
2. Verify there is no Index other search engines option. It should have been removed.

Description

Originally, Chromium would be auto-discovering search engines for sites that people visited. For example, if you went to homedepot.com and did a search, it would save this. When someone went to brave://settings/search, you'd be able to see all the sites they visited and these sites would interfere with the omnibox behavior too.

We had created #14496 to track this and put the logic behind a flag (default disabled). This rework on our side was done with brave/brave-core#9602.

Upstream, this unwanted behavior was tracked with https://issues.chromium.org/issues/40088547. Eventually, the search settings page was reworked and this behavior was removed.

We should also delete our patch as it's not doing anything anymore.