feat(github): add workflow to manage stale issues and PRs (#4871)

Co-authored-by: Jacob Richman <jacob314@gmail.com>

.github/workflows/no-response.yml

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+name: No Response
+
+# Run as a daily cron at 1:45 AM
+on:
+  schedule:
+    - cron: '45 1 * * *'
+  workflow_dispatch: {}
+
+jobs:
+  no-response:
+    runs-on: ubuntu-latest
+    if: ${{ github.repository == 'google-gemini/gemini-cli' }}
+    permissions:
+      issues: write
+      pull-requests: write
+    concurrency:
+      group: ${{ github.workflow }}-no-response
+      cancel-in-progress: true
+    steps:
+      - uses: actions/stale@5bef64f19d7facfb25b37b414482c7164d639639
+        with:
+          repo-token: ${{ secrets.GITHUB_TOKEN }}
+          days-before-stale: -1
+          days-before-close: 14
+          stale-issue-label: 'status/need-information'
+          close-issue-message: >
+            This issue was marked as needing more information and has not received a response in 14 days.
+            Closing it for now. If you still face this problem, feel free to reopen with more details. Thank you!
+          stale-pr-label: 'status/need-information'
+          close-pr-message: >
+            This pull request was marked as needing more information and has had no updates in 14 days.
+            Closing it for now. You are welcome to reopen with the required info. Thanks for contributing!

.github/workflows/stale.yml

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+name: Mark stale issues and pull requests
+
+# Run as a daily cron at 1:30 AM
+on:
+  schedule:
+    - cron: '30 1 * * *'
+  workflow_dispatch: {}
+
+jobs:
+  stale:
+    runs-on: ubuntu-latest
+    if: ${{ github.repository == 'google-gemini/gemini-cli' }}
+    permissions:
+      issues: write
+      pull-requests: write
+    concurrency:
+      group: ${{ github.workflow }}-stale
+      cancel-in-progress: true
+    steps:
+      - uses: actions/stale@5bef64f19d7facfb25b37b414482c7164d639639
+        with:
+          repo-token: ${{ secrets.GITHUB_TOKEN }}
+          stale-issue-message: >
+            This issue has been automatically marked as stale due to 60 days of inactivity.
+            It will be closed in 14 days if no further activity occurs.
+          stale-pr-message: >
+            This pull request has been automatically marked as stale due to 60 days of inactivity.
+            It will be closed in 14 days if no further activity occurs.
+          close-issue-message: >
+            This issue has been closed due to 14 additional days of inactivity after being marked as stale.
+            If you believe this is still relevant, feel free to comment or reopen the issue. Thank you!
+          close-pr-message: >
+            This pull request has been closed due to 14 additional days of inactivity after being marked as stale.
+            If this is still relevant, you are welcome to reopen or leave a comment. Thanks for contributing!
+          days-before-stale: 60
+          days-before-close: 14
+          exempt-issue-labels: pinned,security
+          exempt-pr-labels: pinned,security