feat(ui): add composer Stop and simplify task controls (#13104)

## Thinking Path

> - Paperclip is the open source app people use to manage AI agents for
work.
> - The task composer is where operators direct running agents.
> - Operators need to stop work without leaving the conversation.
> - Existing pause controls already hold task trees and interrupt both
runner types.
> - This pull request connects the composer to those controls and
removes repeated feedback.
> - Operators can pause work quickly and still queue messages while
agents run.

## Linked Issues or Issue Description

**What existing behavior does this improve?**

Task pause, resume, and cancellation in the task page and composer.

**Current behavior**

The empty composer cannot stop a running task. Task controls require
extra confirmation and reason text. Pause can show several notifications
for the task already on screen.

**Proposed behavior**

Show Stop while this task runs and the composer is empty. Text or
attachments switch it to Send. Stop and the menu use the same manual
pause hold. Parent pauses include descendants. Keep task cancellation in
the menu with a compact confirmation. Show one quiet pause row and gray
cancelled-run details.

**Reason and benefit**

Operators can interrupt execution with one click. Drafts and queued
messages keep their existing behavior. The UI waits for actual
termination, including native cancellation acknowledgment.

**Breaking changes**

No endpoint, schema, or task-status change. Pause no longer asks for
confirmation or a reason. Resume now honors the existing wake-agents
option. Task notifications are suppressed for the task and subtree
currently in view.

Related UI work: #8228 changes navigation and composer shortcuts. This
PR covers execution controls. No duplicate Stop-button PR was found. The
change improves existing controls and does not duplicate a roadmap
milestone.

## What Changed

- Add Stop, pending feedback, duplicate-click protection, and inline
errors to the composer.
- Share the pause mutation across the composer, active-run controls, and
menu.
- Poll affected runs after a pause request. Require native cancellation
acknowledgment.
- Remove pause confirmation and shared reason fields. Reduce cancel
confirmation to its task count and actions.
- Honor wake-agents for executable tasks only. Preserve the pause when
recovery review is needed; show partial wake failures inline.
- Preserve explicit legacy reconciliation decisions while their
continuation waits for dispatch.
- Suppress notifications for visible task trees. Use quiet pause and
cancellation feedback.
- Add interactive stories using production controls and native/legacy
end-to-end tests.

## Verification

- User reviewed the running feature and revised Storybooks in the
browser.
- Rebased focused checks passed: 295 original targeted tests, 161
updated route/page/notification/status tests, and 26 recovery
integration tests.
- Both isolated runner journeys pass on the final revision (1.7
minutes). Coverage includes queueing, parent and child interruption,
persisted holds, no automatic continuation, reconciled resume,
cancellation, terminal exclusions, and no Stop toast.
- Native coverage uses real runnerd with a deterministic provider
fixture. Legacy coverage checks actual process termination. Live
hosted-provider execution was not tested.
- Repository typecheck and build, Storybook build, and token gates
passed after rebase. The final server typecheck/build also passed.
- The broad local run completed its general-server stage with 7,219
passing tests, 48 skipped, and two failures from cached pre-fix source
and a stale native provider fixture. Both failed tests pass in fresh
final-head reruns after rebuilding the fixture; the script did not
continue to its later local stages. CI runs all test groups on the final
revision.
- Final revision: all 31 applicable CI checks passed; Storybook visual
regression was skipped by its workflow conditions. Greptile: 5/5, zero
unresolved comments.
- Review `Tasks / Execution Controls` in Storybook. Type and clear a
draft, stop a run, expand cancellation details, and test the menu on
desktop and mobile.

## Risks

- Stop pauses descendants for a parent task. This is the existing pause
contract.
- A held task can remain active if interruption fails. The UI shows an
error instead of claiming termination.
- Resume can start multiple assignees when wake-agents is selected.
Backlog, blocked, and terminal tasks stay excluded. Existing execution
reconciliation remains mandatory where required; Resume never invents
action-outcome evidence.
- Notification suppression uses the visible task and cached subtree.
Notifications for unrelated work remain enabled.

## Model Used

OpenAI GPT-6 through Codex. The exact runtime snapshot and
context-window limit are not exposed in this session. Used reasoning,
tool calls, code execution, and browser inspection.

## 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 tests locally and they pass
- [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>

DESIGN.md

@@ -35,6 +35,14 @@ Existing tiers already in index.css (~80+ tokens) — extraction maps to these o
 7. **Words are part of the system.** One name per concept across the entire UI — the canonical term is *task* (never *issue* or *ticket* in copy, labels, or empty states). Buttons name the action ("Approve hire," not "Submit"). Errors say what happened and what to do. Empty states say what to do first. **Note:** enforcing the task rename is a visible change and is explicitly OUT of the zero-visual-change extraction run; it happens in its own follow-up run.
 8. **Agent-modifiable by design.** The system must be changeable via instructions: single token source, lint rules that enforce it, and this document kept current. A correct change should be expressible as "edit tokens + run checks," not "visit 40 files."
 
+## Contextual feedback
+
+Do not show a toast for task or run state already visible on the current screen.
+This includes descendant runs represented by the open subtree. Show local action
+results in place; keep failures actionable inline. Notifications for other work
+remain useful. Expected cancellation is neutral gray, not an error. A paused
+subtree needs only “Subtree is paused.” and “Resume subtree.”
+
 ## Enforcement (what "compliant" means for the extraction run)
 
 - **Zero visual change is proven, not promised:** Storybook visual snapshots are baselined before any refactor, and all snapshots match baseline after it. A change that alters rendered output must be intentional and human-approved.