REST API: Allow to filter the query in the search controller

[Chouby]

[43739] introduced a new search controller. However, unlike ther controllers, it doesn't propose a convenient way to filter the query.

I propose to add a new filter rest_search_query similar to the filter rest_{$type}_query offered by other controllers.

[audrasjb]

Hi,

5.0.3 is going to be released in a couple of weeks. We are currently sorting the remaining tickets in the milestone. The ticket is sorted in milestone 5.0.3, but requires an @since refresh and a commit/backport to the associated branch. That would be nice to have a refreshed patch asap.

[desrosj]

New filters fall outside of the 5.0.3 scope. Moving to 5.1.

[desrosj]

In 44482:

REST API: Introduce rest_post_search_query filter.

This filter allows the query arguments to be manipulated for a post search query in the REST API.

Props Chouby, swissspidy.
Fixes #45454.