Search: mdBook breaks when hitting `s`

[humitos]

It seems that mdBook listens to s char and we can type it in out own search because it triggers the original mdBook's search.

Steps to reproduce it:

1. Go to https://test-builds.readthedocs.io/en/mdbook/
2. Open the flyout
3. Click on the search input
4. Type testing

You will notice that when pressing the s it will trigger the original mdBook's search and the s char is not written.