chore: Fix test page and flaky test

[jperals]

Description

A leftover useEffect was interfering with tests, causing flakiness.

Also, correctly set loading back to asyncLoading instead of false when closing the dropdown, so that it the page state is correctly reset to its initial state also when asyncLoading is true.

How has this been tested?

• Ran the integration tests 3 times, all successfully
• Manually tested the page to make sure it keeps behaving as expected.

Review checklist

The following items are to be evaluated by the author(s) and the reviewer(s).

Correctness

• Changes include appropriate documentation updates.
• Changes are backward-compatible if not indicated, see CONTRIBUTING.md.
• Changes do not include unsupported browser features, see CONTRIBUTING.md.
• Changes were manually tested for accessibility, see accessibility guidelines.

Security

• If the code handles URLs: all URLs are validated through the checkSafeUrl function.

Testing

• Changes are covered with new/existing unit tests?
• Changes are covered with new/existing integration tests?

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[codecov]

Codecov Report

Patch coverage has no change and project coverage change: -0.02% ⚠️

Comparison is base (c3fe8ad) 93.99% compared to head (3c2b45e) 93.98%.

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #1573      +/-   ##
==========================================
- Coverage   93.99%   93.98%   -0.02%     
==========================================
  Files         649      649              
  Lines       17497    17497              
  Branches     5734     5734              
==========================================
- Hits        16447    16445       -2     
- Misses        981      983       +2     
  Partials       69       69              

see 1 file with indirect coverage changes

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