fix: add actions:write permission to stale workflow

[mnriem]

Problem

The stale workflow marks issues as stale after 150 days but never closes them after the 30-day close window.

Root Cause

actions/stale@v10 uses the GitHub Actions cache to persist state across runs. The workflow only has issues: write and pull-requests: write permissions — it's missing actions: write.

Without that permission, the action can write cache entries but cannot delete them (returns a 403 on cache cleanup):

##[warning]Error delete _state: [403] Resource not accessible by integration

This creates a vicious cycle: once an issue is processed and cached, the action skips it on every future run:

[#96] issue skipped due being processed during the previous run
[#87] issue skipped due being processed during the previous run
[#83] issue skipped due being processed during the previous run
...

So stale issues never reach the closing logic.

Fix

Add actions: write to the workflow permissions block, allowing the stale action to properly manage its cache lifecycle.

Post-Merge

After merging, you may want to clear the existing stale action cache so all issues get reprocessed on the next run:

gh cache list --repo github/spec-kit | grep stale
gh cache delete <cache-key> --repo github/spec-kit

[Copilot]

Pull request overview

This PR fixes the repository’s stale-issues workflow so it can successfully close issues/PRs after the configured close window by granting the workflow permission to manage the GitHub Actions cache state used by actions/stale@v10.

Changes:

• Add actions: write to the permissions block in the stale workflow so the action can delete/cleanup its cache entries and avoid permanently skipping previously processed issues.

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