The actions/stale@v10 action uses GitHub Actions cache to persist state
across runs. Without the actions:write permission, the action can write
cache entries but cannot delete them (403 error on cache cleanup).
This causes a vicious cycle: once an issue is processed and cached, the
action skips it on every future run with 'issue skipped due being
processed during the previous run' - so stale issues never reach the
closing logic after being marked stale.
Adding actions:write allows the action to properly manage its cache
lifecycle, enabling stale issues to be closed after the configured
30-day close window.