chore: tmp skip cache for eslint-plugin lint

[JamesHenry]

• Fixes an existing issue with stale rule configs
• Updates duplicate CI job names
• Disables the cache for linting eslint-plugin to see if the prettier sync flakiness goes away

[typescript-eslint]

Thanks for the PR, @JamesHenry!

typescript-eslint is a 100% community driven project, and we are incredibly grateful that you are contributing to that community.

The core maintainers work on this in their personal time, so please understand that it may not be possible for them to review your work immediately.

Thanks again!

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[nx-cloud]

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✅ Successfully ran 31 targets

• nx test eslint-plugin
• nx test typescript-estree
• nx test scope-manager
• nx test typescript-eslint
• nx test utils
• nx test type-utils
• nx run types:build
• nx test visitor-keys
• nx test repo-tools
• nx run repo-tools:postinstall-script
• nx test parser
• nx test rule-schema-to-typescript-types
• nx run-many --target=build --parallel --exclude=website --exclude=website-eslint
• nx test eslint-plugin --coverage=false
• nx test ast-spec
• nx test eslint-plugin-internal
• nx run-many --target=lint --parallel --exclude eslint-plugin
• nx run integration-tests:test
• nx test typescript-estree --coverage=false
• nx run-many --target=typecheck --parallel
• nx test scope-manager --coverage=false
• nx test typescript-eslint --coverage=false
• nx test ast-spec --coverage=false
• nx test type-utils --coverage=false
• nx test rule-schema-to-typescript-types --coverage=false
• nx test visitor-keys --coverage=false
• nx test eslint-plugin-internal --coverage=false
• nx test utils --coverage=false
• nx test parser --coverage=false
• nx test repo-tools --coverage=false
• nx run repo-tools:generate-configs

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[JoshuaKGoldberg]

For tracking: #8373

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 87.69%. Comparing base (fb82a33) to head (6eecaa5).
Report is 2 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #8539      +/-   ##
==========================================
+ Coverage   86.92%   87.69%   +0.77%     
==========================================
  Files         251      397     +146     
  Lines       12250    13841    +1591     
  Branches     3864     4072     +208     
==========================================
+ Hits        10648    12138    +1490     
- Misses       1332     1403      +71     
- Partials      270      300      +30     

Flag	Coverage Δ
unittest	87.69% <ø> (+0.77%)	⬆️

Flags with carried forward coverage won't be shown. Click here to find out more.

see 149 files with indirect coverage changes

[JoshuaKGoldberg]

💚