Add a stale workflow for PRs #1120

Hi @andrewdennis117 — could you set up a Stale Workflow for pull requests on coder/registry, similar to how we do it on coder/coder?

Context

coder/coder already runs an actions/stale workflow (see .github/workflows/stale.yaml). coder/registry currently has no stale handling — its workflows are only: check_registry_site_health.yaml, ci.yaml, deploy-registry.yaml, golangci-lint.yml, module-scorecard-check.yaml, module-scorecards.yaml, release.yml, version-bump.yaml, zizmor.yaml.

Requested behavior

• Automatically mark PRs as stale when there is no user reply and the last message on the PR is not from the user for a certain amount of time.
• Follow the same conventions as coder/coder's stale workflow:
  • stale-pr-label: "stale"
  • PRs become stale after ~7 days of inactivity, close ~3 days later
  • Empty stale/close messages to avoid cluttering PRs (stale-pr-message: "")
  • operations-per-run and ascending to stay within the API limit and process oldest first
• days-before-stale on the issue side is effectively disabled (3650) on coder/coder while they work through polish issues — worth deciding whether the registry needs the same.

Notes

• Need to decide the exact "no user reply / last message not from the user" detection: the plain actions/stale action keys off last-updated-at, not "who wrote the last comment." If we want that precise condition, it may need a custom step (e.g. actions/github-script) to inspect the latest comment author before marking stale.
• Also confirm thresholds (days before stale / close) the registry team wants.

Deliverables

• .github/workflows/stale.yaml in coder/registry
• stale label created (or auto-created by the action)

cc @matifali @bpmct