[Backport 2.x] Saved queries new UI (#8469)

[amsiglan]

Description

Backport #8469 to 2.x

Check List

• All tests pass
  • yarn test:jest
  • yarn test:jest_integration
• New functionality includes testing.
• New functionality has been documented.
• Update CHANGELOG.md
• Commits are signed per the DCO using --signoff

[github-actions]

❌ Invalid Changelog Heading

The '## Changelog' heading in your PR description is either missing or malformed. Please make sure that your PR description includes a '## Changelog' heading with proper spelling, capitalization, spacing, and Markdown syntax.

[codecov]

Codecov Report

Attention: Patch coverage is 7.04846% with 211 lines in your changes missing coverage. Please review.

Project coverage is 60.84%. Comparing base (ac7bf02) to head (2773848).
Report is 8 commits behind head on 2.x.

Files with missing lines	Patch %	Lines
...lugins/data/public/ui/saved_query_form/helpers.tsx	0.00%	64 Missing ⚠️
...ui/saved_query_flyouts/open_saved_query_flyout.tsx	0.00%	63 Missing ⚠️
...public/ui/saved_query_flyouts/saved_query_card.tsx	0.00%	42 Missing ⚠️
...ry_management/saved_query_management_component.tsx	21.42%	10 Missing and 1 partial ⚠️
...ta/public/query/saved_query/saved_query_service.ts	56.25%	4 Missing and 3 partials ⚠️
...ublic/ui/saved_query_flyouts/save_query_flyout.tsx	0.00%	7 Missing ⚠️
...c/plugins/data/public/ui/search_bar/search_bar.tsx	0.00%	5 Missing ⚠️
...ugins/data/public/ui/filter_bar/filter_options.tsx	0.00%	2 Missing and 2 partials ⚠️
src/plugins/data/public/plugin.ts	0.00%	3 Missing ⚠️
...ata/public/ui/saved_query_form/save_query_form.tsx	0.00%	3 Missing ⚠️
... and 2 more

Additional details and impacted files

@@            Coverage Diff             @@
##              2.x    #8705      +/-   ##
==========================================
- Coverage   60.93%   60.84%   -0.10%     
==========================================
  Files        3792     3797       +5     
  Lines       90507    90671     +164     
  Branches    14209    14251      +42     
==========================================
+ Hits        55153    55168      +15     
- Misses      31868    32012     +144     
- Partials     3486     3491       +5     

Flag	Coverage Δ
Linux_1	29.07% <8.69%> (-0.01%)	⬇️
Linux_2	56.53% <ø> (ø)
Linux_3	37.60% <7.04%> (-0.11%)	⬇️
Linux_4	29.95% <8.69%> (-0.01%)	⬇️
Windows_1	29.10% <8.69%> (+0.01%)	⬆️
Windows_2	56.49% <ø> (ø)
Windows_3	37.60% <7.04%> (-0.10%)	⬇️
Windows_4	29.95% <8.69%> (-0.01%)	⬇️

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[virajsanghvi]

approving assuming ci passes

[github-actions]

❌ Invalid Changelog Heading

The '## Changelog' heading in your PR description is either missing or malformed. Please make sure that your PR description includes a '## Changelog' heading with proper spelling, capitalization, spacing, and Markdown syntax.