`use_sticky_comment` has no effect in agent mode — MCP server starts without CLAUDE_COMMENT_ID

**Describe the bug**

When `use_sticky_comment: true` is set but the action enters agent mode (because `track_progress: false` and a `prompt` is provided), the sticky comment feature silently breaks. No comment is ever created on the PR, even though the MCP comment server is included in the tool list.

The root cause is a code path gap in `src/modes/agent/index.ts`:

1. `detectMode()` in `src/modes/detector.ts` returns `"agent"` when `track_progress` is false and `prompt` is set
2. In `src/modes/agent/index.ts` line 105, `claudeCommentId` is hardcoded to `undefined`
3. Even though `shouldIncludeCommentServer` evaluates to `true` in `install-mcp-server.ts` (because `mcp__github_comment__update_claude_comment` is in `allowedTools`), the MCP server starts without `CLAUDE_COMMENT_ID` in its environment
4. Every call to `update_claude_comment` fails at line 42-44 of `github-comment-server.ts` with: `"CLAUDE_COMMENT_ID environment variable is required"`

Unlike tag mode, agent mode never calls `createInitialComment()` to create the comment and obtain its ID.

**To Reproduce**

1. Configure a workflow with `track_progress: false`, `use_sticky_comment: true`, and a `prompt` on a `pull_request` event (e.g., with `types: [labeled]`)
2. Trigger the action by adding the label to a PR
3. The action runs successfully (Claude executes the prompt and produces output)
4. No sticky comment appears on the PR

**Expected behavior**

When `use_sticky_comment: true`, agent mode should create an initial comment (like tag mode does via `createInitialComment()`) and pass the resulting comment ID to the MCP server via `CLAUDE_COMMENT_ID`. The sticky comment should be updated throughout the run.

**Workflow yml file**

```yaml
on:
pull_request:
types: [labeled]

jobs:
review:
if: github.event.label.name == 'claude-review'
runs-on: ubuntu-latest
steps:
- uses: anthropics/claude-code-action@v1
with:
anthropic_api_key: ${{ secrets.ANTHROPIC_API_KEY }}
use_sticky_comment: true
prompt: |
Review this pull request and post your findings as a comment.
```

Because `track_progress` defaults to `false` and `prompt` is set, this enters agent mode where the sticky comment is silently ignored.

**API Provider**

[x] Anthropic First-Party API (default)
[ ] AWS Bedrock
[ ] GCP Vertex

**Additional context**

- **Workaround:** Setting `track_progress: true` forces tag mode where sticky comments work, but this isn't viable for all event types (e.g., `labeled` fails `validateTrackProgressEvent`).
- **Suggested fix:** In `agent/index.ts`, when `context.inputs.useStickyComment` is true and the context is a PR or issue, call `createInitialComment()` and pass the resulting ID as `claudeCommentId` to `prepareMcpConfig`.
- **Possibly related:** #1052 may be a downstream symptom of this same root cause — the review result is captured but never posted because the comment server silently fails.

Start in src/modes/agent/index.ts, then compare the agent path with tag mode and trace detectMode() in src/modes/detector.ts, prepareMcpConfig in install-mcp-server.ts, and the environment check in github-comment-server.ts. Done means a PR or issue run with use_sticky_comment enabled creates the initial comment, passes its ID to the MCP server, and updates that comment successfully.

Written by the indexing model from the issue text.