[codex] Add ask issue work mode (#8334)

## Thinking Path

> - Paperclip is the open source app people use to manage AI agents for
work.
> - Issue work mode controls how a task starts and how the conversation
composer frames the operator's intent.
> - Paperclip already supports standard agent execution and planning
mode, but there is no lightweight mode for asking a question without
immediately implying execution or plan drafting.
> - That gap makes low-commitment clarification workflows look like
normal task execution.
> - This pull request adds an explicit Ask mode and threads it through
shared contracts, server heartbeat context, and the issue composer UI.
> - The benefit is that operators can create or switch a task into a
question-oriented mode while preserving existing agent and planning
flows.

## Linked Issues or Issue Description

No public GitHub issue exists for this change. Inline feature request
follows the repository feature request template.

### Subsystem affected

Cross-cutting: `packages/shared`, `server/`, and `ui/`.

### Problem or motivation

Issue conversations currently distinguish standard agent work from
planning work, but question-first conversations do not have a clear
public mode in the shared contract or UI. Operators who want to ask an
agent a focused question have to use standard mode, which can imply
normal task execution, or planning mode, which asks for a plan rather
than an answer.

### Proposed solution

Add Ask as a first-class issue work mode. It should be selectable from
issue creation and issue chat, cycle alongside Standard and Planning
from the keyboard shortcut/menu, appear distinctly in composer styling,
and be included in heartbeat context so agents know to answer directly
instead of executing or drafting a plan.

### Alternatives considered

- Keep using standard mode for questions: rejected because it does not
communicate answer-only intent to the agent or the UI.
- Reuse planning mode for questions: rejected because planning mode asks
for a plan and is semantically different from asking a question.
- Add only local UI copy: rejected because the mode needs to be
represented in the shared contract and server heartbeat context to be
reliable.

### Roadmap alignment

This is a focused issue-workflow improvement. `ROADMAP.md` was checked
and no duplicate planned core work was found.

### Additional context

Related public searches performed before opening this PR:

- GitHub PR search for `"ask mode" repo:paperclipai/paperclip`
- GitHub issue search for `"ask mode" repo:paperclipai/paperclip`
- GitHub PR search for `"work mode" "ask" repo:paperclipai/paperclip`

No duplicate PR was found.

## What Changed

- Added `ask` to the shared issue work-mode contract and validation
coverage.
- Included issue work mode in heartbeat context summaries so agents can
see standard, planning, and ask state.
- Added Ask mode metadata, styling, composer tone handling, and
selection/cycling behavior in the issue chat/new issue UI.
- Updated focused tests for shared validators, heartbeat context, and
affected UI work-mode flows.

## Verification

- `NODE_ENV=test pnpm exec vitest run
ui/src/components/ChatComposer.test.tsx
ui/src/components/IssueChatThread.test.tsx
ui/src/components/NewIssueDialog.test.tsx
ui/src/lib/work-mode-meta.test.ts`
- `NODE_ENV=test pnpm exec vitest run
packages/shared/src/validators/issue.test.ts
server/src/__tests__/heartbeat-context-summary.test.ts
server/src/__tests__/issues-service.test.ts
ui/src/components/ChatComposer.test.tsx
ui/src/components/IssueChatThread.test.tsx
ui/src/components/NewIssueDialog.test.tsx
ui/src/lib/work-mode-meta.test.ts ui/src/pages/IssueDetail.test.tsx`

The broader targeted command passed 8 test files / 245 tests.

Visual reference for Standard/Planning/Ask composer states:
https://gist.github.com/cryppadotta/714d8590bac55500a65e7e16de5bb4b8

It emitted an expected warning from an existing server test fixture
about a missing run-log fixture while verifying derived issue comment
metadata.

## Risks

Low to moderate risk. This adds a new enum value that crosses shared,
server, and UI contracts. Existing standard and planning modes are
preserved, but any downstream code assuming only two non-terminal work
modes may need to handle `ask`.

> 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 GPT-5 Codex coding agent in Paperclip CodexCoder mode, with
shell, git, GitHub connector, and local test execution tools. Context
window and exact hosted model snapshot are not exposed in this 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 searched GitHub for duplicate or related PRs and linked
them above
- [x] I have either (a) linked existing issues with `Fixes: #` / `Closes
#` / `Refs #` OR (b) described the issue in-PR following the relevant
issue template
- [x] I have not referenced internal/instance-local Paperclip issues or
links (only public GitHub `#NNN` / `github.com/paperclipai/paperclip`
URLs)
- [ ] My branch name describes the change (e.g. `docs/...`, `fix/...`,
`feat/...`) and contains no internal Paperclip ticket id or
instance-derived details
- [x] I have run tests locally and they pass
- [x] I have added or updated tests where applicable
- [x] 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] All Paperclip CI gates are green
- [x] Greptile is 5/5 with no open P2s, recommendations, or follow-ups
- [x] I will address all Greptile and reviewer comments before
requesting merge

---------

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

server/src/services/heartbeat.ts

@@ -2886,7 +2886,14 @@ export function buildPaperclipTaskMarkdown(input: {
       `- Issue: ${quoteTaskScalar(issue.identifier || issue.id)}`,
       `- Title: ${quoteTaskScalar(issue.title)}`,
     );
-    if (issue.workMode === "planning") {
+    if (issue.workMode === "ask") {
+      lines.push(
+        `- Work mode: ${quoteTaskScalar("ask")}`,
+        "",
+        "Ask mode directive:",
+        "Answer the question directly in the issue thread. Do not write implementation code, and do not produce an implementation plan. Use tools only for investigation or temporary scratch work when needed; the deliverable is the answer.",
+      );
+    } else if (issue.workMode === "planning") {
       let directive = "Make the plan only. Do not write code or perform implementation work.";
       if (wakeComment) {
         directive = "Update the plan only. Do not write code or perform implementation work.";