Using browser navigation on search page does not always clear query input and streams input.

## Description

https://github.com/Graylog2/graylog2-server/pull/24538 restores the behavior to navigate between searches using the browser navigation. This works well in most cases except the following:

1. Open the search page and execute a search without a stream and query
2. Define a query, select a stream and execute the search again.
3. Navigate back to the initial search.

Step 3 will not clear the stream select and query. Fixing this bug requires more fundamental changes.

There seems to be a related regression.
Step 4: add a character to the query which is still in the query input and execute the search. You will see that the URL query params no longer update at all.

* Graylog Version: It looks like this has always been a problem

## Checklist
- [x] This issue fix need to be backported.
- [ ] Does this issue have **security** implications?