Jetpack Search prevents URL filtering

1. Go to a WordPress site with Jetpack Search enabled and type into the URL /author/authorname?s=searchterm
2. Jetpack Search will take over the search because of the ?s= param but will not honor the URL filter of author name

#### What I expected
Normally, WordPress Core allows you to search within authors, tags, categories, or on WordPress.com mentions. This allows you to quickly find something buy typing jesse.blog/category/articles/?s=Jetpack. This URL would automatically allow me to see results for the query "Jetpack" for posts that are categorized in "articles".

#### What happened instead
Jetpack Search grabs the search param and just shows me the results for the entire site without filtering down into the URL filtered param.

**Screenshots**

These results are not authored by the user "jesserfriedman"

Reproduce the issue from the URL entry point `/author/authorname?s=searchterm` on a WordPress site with Jetpack Search enabled, then compare it with the category URL example in the report. Trace the Jetpack Search integration that takes over the `?s=` query and verify completion when author, category, tag, and similar URL filters remain applied to results.

Written by the indexing model from the issue text.