fix(docs): update GitHub Action docs to match ambient-action v0.0.5 (#1233)

<!-- acp:session_id=session-bce2475a-27ed-44ff-9b77-e0b522fc111d
source=#1232 last_action=2026-04-07T15:34:00Z retry_count=2 -->

## Summary
- Updates GitHub Action docs to reflect the current `ambient-action`
`action.yml` (v0.0.5)
- Adds new inputs: `session-name`, `stop-on-run-finished`,
`poll-timeout`
- Adds new output: `session-url`
- Fixes `timeout` description (now inactivity timeout in seconds,
default `0`) and renames old polling timeout to `poll-timeout`
- Updates all example version refs from `v0.0.2` to `v0.0.5`
- Adds new "Send to existing session" mode and example
- Updates bugfix workflow doc to use `v0.0.5` and `poll-timeout`

Closes #1232

## Test plan
- [x] Docs build passes (`npm run build` in `docs/`)
- [ ] Visual review of rendered pages

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-authored-by: Ambient Code Bot <bot@ambient-code.local>
Co-authored-by: Claude Opus 4.6 <noreply@anthropic.com>

Author: 3 people

docs/src/content/docs/extensions/github-action.md

@@ -6,30 +6,34 @@ import { Badge } from '@astrojs/starlight/components';
 
 <Badge text="Beta" variant="caution" />
 
-The [`ambient-action`](https://github.com/ambient-code/ambient-action) GitHub Action (v0.0.2) creates Ambient Code Platform sessions directly from GitHub workflows. Use it to automate bug fixes on new issues, run code analysis on pull requests, or trigger any agent workflow from CI/CD.
+The [`ambient-action`](https://github.com/ambient-code/ambient-action) GitHub Action creates Ambient Code Platform sessions directly from GitHub workflows. Use it to automate bug fixes on new issues, run code analysis on pull requests, or trigger any agent workflow from CI/CD.
 
 ## Modes
 
 - **Fire-and-forget** -- Create a session and move on. The workflow does not wait for the session to finish.
 - **Wait-for-completion** -- Create a session and poll until it completes (or times out). Useful when subsequent steps depend on the agent's output.
+- **Send to existing session** -- Send a message to a running session instead of creating a new one (set `session-name`).
 
 ## Inputs
 
 | Input | Required | Default | Description |
 |-------|----------|---------|-------------|
-| `api-url` | Yes | -- | Ambient Code Platform API URL |
-| `api-token` | Yes | -- | Bearer token for authentication (store as a GitHub secret) |
+| `api-url` | Yes | -- | Ambient Code Platform backend API URL |
+| `api-token` | Yes | -- | Bot user bearer token for authentication (store as a GitHub secret) |
 | `project` | Yes | -- | Target workspace/project name |
-| `prompt` | Yes | -- | Task prompt for the agent |
+| `prompt` | Yes | -- | Initial prompt for the session, or message to send to an existing session |
+| `session-name` | No | -- | Existing session name to send a message to (skips session creation) |
 | `display-name` | No | -- | Human-readable session display name |
 | `repos` | No | -- | JSON array of repo objects (`[{"url":"...","branch":"...","autoPush":true}]`) |
 | `labels` | No | -- | JSON object of labels for the session |
 | `environment-variables` | No | -- | JSON object of environment variables to inject into the runner |
 | `workflow` | No | -- | JSON workflow object (e.g., `{"gitUrl":"https://...","branch":"main","path":"workflows/my-wf"}`) |
 | `model` | No | -- | Model override (e.g., `claude-sonnet-4-20250514`) |
+| `timeout` | No | `0` | Session inactivity timeout in seconds -- auto-stops after this duration of inactivity (`0` means no timeout) |
+| `stop-on-run-finished` | No | `false` | Stop the session automatically when the agent finishes its run |
 | `wait` | No | `false` | Wait for session completion |
-| `timeout` | No | `30` | Session timeout in minutes |
 | `poll-interval` | No | `15` | Seconds between status checks (only when `wait: true`) |
+| `poll-timeout` | No | `60` | Maximum minutes to poll before giving up (only when `wait: true`) |
 | `no-verify-ssl` | No | `false` | Disable SSL certificate verification (for self-signed certs) |
 
 ## Outputs
@@ -38,6 +42,7 @@ The [`ambient-action`](https://github.com/ambient-code/ambient-action) GitHub Ac
 |--------|-------------|
 | `session-name` | Name of the created session |
 | `session-uid` | UID of the created session |
+| `session-url` | URL to the session in the Ambient UI |
 | `session-phase` | Final session phase (only set when `wait: true`) |
 | `session-result` | Session result text (only set when `wait: true`) |
 
@@ -55,7 +60,7 @@ jobs:
   triage:
     runs-on: ubuntu-latest
     steps:
-      - uses: ambient-code/ambient-action@v0.0.2
+      - uses: ambient-code/ambient-action@v0.0.5
         with:
           api-url: ${{ secrets.ACP_URL }}
           api-token: ${{ secrets.ACP_TOKEN }}
@@ -71,22 +76,36 @@ jobs:
 Set `wait: true` to block the workflow until the session finishes:
 
 ```yaml
-- uses: ambient-code/ambient-action@v0.0.2
+- uses: ambient-code/ambient-action@v0.0.5
   with:
     api-url: ${{ secrets.ACP_URL }}
     api-token: ${{ secrets.ACP_TOKEN }}
     project: my-team
     prompt: "Analyze the codebase for security vulnerabilities and report findings."
     wait: true
-    timeout: 30
+    poll-timeout: 30
+```
+
+## Send a message to an existing session
+
+Use `session-name` to send a follow-up prompt to a running session instead of creating a new one:
+
+```yaml
+- uses: ambient-code/ambient-action@v0.0.5
+  with:
+    api-url: ${{ secrets.ACP_URL }}
+    api-token: ${{ secrets.ACP_TOKEN }}
+    project: my-team
+    session-name: my-existing-session
+    prompt: "Run the test suite again and report the results."
 ```
 
 ## Multi-repo sessions
 
 Pass a JSON array to clone multiple repositories into the session:
 
 ```yaml
-- uses: ambient-code/ambient-action@v0.0.2
+- uses: ambient-code/ambient-action@v0.0.5
   id: session
   with:
     api-url: ${{ secrets.ACP_URL }}
@@ -101,7 +120,7 @@ Pass a JSON array to clone multiple repositories into the session:
     workflow: |
       {"gitUrl": "https://github.com/org/workflows.git", "branch": "main", "path": "workflows/cross-repo-refactor"}
     wait: true
-    timeout: 45
+    poll-timeout: 45
 
 - run: echo "Session ${{ steps.session.outputs.session-name }} finished"
 ```

docs/src/content/docs/workflows/bugfix.md

@@ -348,7 +348,7 @@ jobs:
     if: github.event.label.name == 'auto-fix'
     runs-on: ubuntu-latest
     steps:
-      - uses: ambient-code/ambient-action@v0.0.2
+      - uses: ambient-code/ambient-action@v0.0.5
         with:
           api-url: ${{ secrets.ACP_URL }}
           api-token: ${{ secrets.ACP_TOKEN }}
@@ -360,7 +360,7 @@ jobs:
           workflow: |
             {"gitUrl": "https://github.com/ambient-code/workflows", "branch": "main", "path": "workflows/bugfix"}
           wait: true
-          timeout: 30
+          poll-timeout: 30
 ```
 
 When `wait` is `true`, the action outputs `session-name`, `session-uid`,