"Reset filters" should also reset the search input

[Zerotask]

Do you have any examples?

Is it a third party application feature request?

No

Describe your feature request

If you search for something which has no results, you see the "No results found" template, with the buttons to create a new object and reset filters. Clicking on "Reset filters" does not reset the search input, although you might expect it, since a search is also some sort of filtering, even though it's not part of the filters block.
Therefore I suggest, that "Reset filters" also clears the search input.

[Zerotask]

Another thing I noticed is, that the search input on the objects page has no type, which means it defaults to type="text", whereas the search on the left side menu is type="search":

type="search" offers, besides better accessibility, also this little icon to clear the input.

Therefore I suggest to make this search look and behave the same as the left side menu search

[KUMA-ORIGINAL]

I support this suggestion.
From a user's perspective, the search input behaves like a filter — it's applied alongside other filters and influences the result set.
If "Reset filters" clears all active filters, it makes perfect sense for it to also clear the search query, since it's part of what narrowed down the results.

This would improve UX and make the "Reset filters" button more intuitive and complete in its behavior.

[lukasvinclav]

@Zerotask I believe this one should fix your issue #1334