auto create pr to update helm index when release chart

[chaosi-zju]

What type of PR is this?

/kind feature

What this PR does / why we need it:

Auto create pr to update helm index when release chart.

You can see the effective demonstration in my personal repo:

• BuildRelease action: https://github.com/chaosi-zju/karmada/actions/runs/12228744816
• Auto submited pr: Bump upgrade helm chart index to v1.12.12 chaosi-zju/karmada#17

Which issue(s) this PR fixes:

Fixes #

Special notes for your reviewer:

I investigated the helm/chart-releaser-action. It generates Helm chart releases and updates the chart index on the gh-pages branch, but this is not what we need:

• We already have ci process to generate and upload chart release assets, we don't need another ci to do the same thing.
• That chart-releaser-action still need someone to submit a pr to update charts/karmada/Chart.yaml, in order to trigger the process of this action. However, I think it would be better if the operation of update index can be just right triggered by publishing release without anyone manually submit any pr.
• That chart-releaser-action requires a additional branch gh-pages.

So, we just only need a CI process that automatically updates the chart index when a new release is published.

Does this PR introduce a user-facing change?:

[karmada-bot]

[APPROVALNOTIFIER] This PR is NOT APPROVED

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[chaosi-zju]

Attention: to run this action in workflow, the workflow permissions of Allow GitHub Actions to create and approve pull requests should be opened.

[chaosi-zju]

hi @a7i , can you give some advices on this PR, thank you very much~

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Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 47.95%. Comparing base (a655c45) to head (1d7f466).
Report is 14 commits behind head on master.

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Additional details and impacted files

@@            Coverage Diff             @@
##           master    #5911      +/-   ##
==========================================
+ Coverage   47.86%   47.95%   +0.08%     
==========================================
  Files         663      663              
  Lines       54761    54769       +8     
==========================================
+ Hits        26210    26262      +52     
+ Misses      26845    26801      -44     
  Partials     1706     1706              

Flag	Coverage Δ
unittests	47.95% <ø> (+0.08%)	⬆️

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[a7i]

/lgtm 🏆

[chaosi-zju]

@RainbowMango So, you prefer how we move this forward, is add hack/update-chart-index.sh to Build Release pipeline, or I just write a website doc like (cherry-picks )[https://karmada.io/docs/contributor/cherry-picks] about how to use hack/update-chart-index.sh to auto create a PR to update chart index?