[codex] Surface live run comment context (#4957)

## Thinking Path

> - Paperclip orchestrates AI agents through issue comments and
heartbeat runs
> - The board UI needs to distinguish a comment that triggered a live
run from comments queued after that run started
> - The run payload already stores comment context, but active-run API
responses did not expose the ids the UI needs
> - Without those ids, the triggering comment can flash as queued while
the agent is already responding to it
> - This pull request exposes live-run comment context and teaches the
optimistic comment helper to ignore the trigger comment
> - The benefit is clearer issue-chat state during comment-triggered
agent interruptions

## What Changed

- Added `contextCommentId` and `contextWakeCommentId` to active/live run
payloads.
- Threaded those ids through server routes, heartbeat summaries, UI API
types, and issue detail rendering.
- Updated optimistic comment classification to avoid marking the
triggering comment as queued.
- Added server and UI regression coverage.

## Verification

- `pnpm exec vitest run
server/src/__tests__/agent-live-run-routes.test.ts
ui/src/lib/optimistic-issue-comments.test.ts`

## Risks

- Low-to-medium risk: adds optional fields to existing run payloads.
Existing consumers should ignore unknown fields, and UI handling is
null-safe.

> For core feature work, check [`ROADMAP.md`](ROADMAP.md) first and
discuss it in `#dev` before opening the PR. Feature PRs that overlap
with planned core work may need to be redirected — check the roadmap
first. See `CONTRIBUTING.md`.

## Model Used

- OpenAI Codex, GPT-5 coding agent, tool use and local command
execution. Exact context window was not exposed in the runtime.

## Checklist

- [x] I have included a thinking path that traces from project context
to this change
- [x] I have specified the model used (with version and capability
details)
- [x] I have checked ROADMAP.md and confirmed this PR does not duplicate
planned core work
- [x] I have run tests locally and they pass
- [x] I have added or updated tests where applicable
- [ ] If this change affects the UI, I have included before/after
screenshots
- [x] I have updated relevant documentation to reflect my changes
- [x] I have considered and documented any risks above
- [x] I will address all Greptile and reviewer comments before
requesting merge

---------

Co-authored-by: Paperclip <noreply@paperclip.ing>

ui/src/api/heartbeats.ts

@@ -19,6 +19,8 @@ export interface ActiveRunForIssue {
   status: string;
   invocationSource: string;
   triggerDetail: string | null;
+  contextCommentId?: string | null;
+  contextWakeCommentId?: string | null;
   startedAt: string | Date | null;
   finishedAt: string | Date | null;
   createdAt: string | Date;
@@ -41,6 +43,8 @@ export interface LiveRunForIssue {
   status: string;
   invocationSource: string;
   triggerDetail: string | null;
+  contextCommentId?: string | null;
+  contextWakeCommentId?: string | null;
   startedAt: string | null;
   finishedAt: string | null;
   createdAt: string;