fix(tasks): require resume before sending to paused tasks (#13232)

## Thinking Path

> - Paperclip is the open source app people use to manage AI agents for
work.
> - Task execution controls let board users pause a task or its subtree.
> - The composer still accepted messages while a pause hold was active.
> - A paused task must require an explicit resume before the user can
send another message.
> - This pull request replaces the composer with an amber pause card and
checks board comment writes on the server.
> - The user keeps their draft and resumes through the existing task
controls.

## Linked Issues or Issue Description

Refs #13104. Refs #13119.

**What existing behavior does this improve?**

The task composer and existing task/subtree pause controls.

**Current behavior**

A paused task can still receive a board message. The pause notice sits
outside the composer, which leaves the send action available.

**Proposed behavior**

Show an amber takeover in both task chat and the classic composer.
Preserve the draft. Require the user to resume the task or the ancestor
subtree before sending. Reject board comment writes through either
supported write route while the pause hold is active.

**Breaking changes**

Board comment writes to a paused task now return HTTP 409. Agent run
reports remain supported during a pause. There is no schema migration.

## What Changed

- Add a shared amber composer takeover with task, subtree, saved draft,
pending, and error states.
- Use effective ancestor pause state in both composer interfaces.
Refresh it after pause events, task updates, and rejected sends.
- Preserve draft text and attachments. Hide editor, send, queued edit,
and pending question controls while paused.
- Check active pause holds before board comment writes can mutate tasks,
store comments, or wake agents.
- Connect the approved Storybook examples to the production component
and update the design and behavior docs.
- Add browser coverage for both composers, draft persistence, resume,
inherited holds, and rejected writes. Update ACP continuation coverage
for the explicit resume requirement.

## Verification

- Passed: `pnpm -r typecheck`.
- Passed: `pnpm build`.
- Passed: `pnpm build-storybook`.
- Passed: `pnpm check:token-gates` and `git diff --check`.
- Passed: focused UI tests (398 tests) and server route tests (127
tests).
- Passed: `pnpm exec playwright test --config
tests/e2e/playwright.config.ts tests/e2e/paused-composer.spec.ts
tests/e2e/acp-stop-continuation.spec.ts` (5 tests).
- Passed: manual browser walkthrough in a disposable local instance.
Pause with a draft, refresh while paused, resume, send, and reopen. The
draft returned, and one message persisted. The amber card and resume
dialog were readable with no clipping.
- Full local `pnpm test:run` did not pass: the general-server stage
recorded 9,072 passing tests, 6 database setup failures from macOS
shared-memory exhaustion, and 4 failed tests. This stopped the script
before its later groups. Latest-head CI runs those groups independently.
- Local follow-up: the Git file-resource load test passed on rerun (4
tests); native finalization migration passed after clearing the
abandoned browser-test database allocation. Building the native debug
fixtures fixed the missing fake provider. The remaining native-session
recovery assertion also reproduces on untouched base commit `87b3e5fc6`
(36 pass, 1 fail on both base and PR). It expects a settled-session
error but receives a semantic-input-digest error.
- The final UI build, UI typecheck, token gates, both thread suites (182
tests), and all five browser tests passed after the queued-action review
fix. All 31 latest-head CI checks passed, including all server,
workspace, browser, build, release, and security gates. Two optional
Storybook jobs were skipped by workflow policy. Greptile reviewed
`32d8fb5f5` at 5/5 with no open findings.
- Review the Paused Composer and Tasks / Execution Controls stories.
Pause a task with a draft, verify the amber card, resume, and verify the
draft can be sent once.

## Risks

- Clients that used board comments to continue paused work must resume
first. The response is an explicit HTTP 409.
- Pause state can change while a page is open. Live updates refresh the
composer, and the server rejects stale sends before their side effects.
- Resume keeps the existing dialog and optional agent wake behavior.
Agent reports from interrupted runs remain allowed.

## Model Used

OpenAI Codex, based on GPT-6, assisted with design, implementation, code
execution, and browser verification. The exact runtime model ID and
context window are not exposed in this session. The agent used reasoning
and tool calls.

## 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)
- [x] My branch name describes the change (e.g. `docs/...`, `fix/...`)
and contains no internal Paperclip ticket id or instance-derived details
- [x] I have run the relevant tests locally and they pass; the full
local-suite limits are documented above
- [x] I have added or updated tests where applicable
- [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>

doc/SPEC-implementation.md

@@ -21,6 +21,9 @@ Paperclip V1 must provide a full control-plane loop for autonomous agents:
 4. All work is tracked through tasks/comments with audit visibility.
 5. Token/cost usage is reported and budget limits can stop work.
 6. The board can intervene anywhere (pause agents/tasks, override decisions).
+   An effective task or ancestor pause replaces the message composer with an
+   amber Resume takeover. New board messages, including updates with comments,
+   are rejected until the hold is released. Drafts survive pause and resume.
 
 Success means one operator can run a small AI-native company end-to-end with clear visibility and control.