webhtml: fill search input from url parameter

[yktakaha4]

Thank you for this great tool and maintainers.

I think it would be more convenient if the conditions were restored to the text box when performing a search in the webui.
I think this fix will make exploratory searches easier.

This is a sample when accessing http://localhost:2345/ui/?f=%5Emain

Currently, search inputs are cleared every time the page is refreshed.

I checked CONTRIBUTING.md and wanted to write a test, but there was no existing test suite or framework, so I didn't create one.

The PR below seems to partially writing test on the front end, so should I refer to it?
I would like to hear the opinions of reviewers.
#802