Add a « search in api docs » in readthedocs search bar

[tristanlatr]

But also we should investigate the option of adding a « search in api docs » button from the readthedocs search bar.

I think that this can be done in 2 steps:

1. Have pydoctor generate a dedicated search-results.html page that takes the search term from the URL. The important part to allow search input from the URL, not only via typing.

2. Create a raw HTML element on any Sphinx page with a form field that will make a GET to that page.

Originally posted by @adiroiban in https://github.com/twisted/pydoctor/issues/608#issuecomment-1190829555

[tristanlatr]

Maybe we can change the place of the search help as well, create another page just for that.