Update filtered search bar tests for vue 3

What does this MR do and why?

Update filtered search bar tests for vue 3

• bring them partially up to current standards
• remove vue 3 deprecated patterns
• reimplement !144947 (merged), but fix the issue with the FOSS tests by changing storage key to one in CE
  • previously the storage key requirements was used in the test, but that is only available in EE
  • the second commit is the fix

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Related to #391171

Related to !144947 (merged)