feat(app): float composer trackers as pills over the transcript (#3482)

The subagents track and the task list were stacked cards above the
composer. Each one pushed the composer further down the pane and painted
an opaque band the timeline stopped at, and both spent a full row on a
count that fits in a pill.

Both are now pills that open a panel — a popover on wide screens, a sheet
on compact ones, from the existing menu engine rather than a fourth
floating-panel implementation. The row frame is shared, so a subagent row
and a task row sit on the same rail whatever their contents.

The bar mounts inside the transcript's animated container and pins itself
to the bottom edge, so scrolled content passes under the pills instead of
stopping above them. It stays a child of that container rather than a
sibling floating over the composer: on Android a view outside its parent's
bounds paints but takes no touches, and every pill is pressable. The
container carries the same keyboard transform the composer does, so the
pills track the composer's top edge when the keyboard moves.

The tracker state moves out of the composer with it. None of it was
composer state; it lived there because that is where it used to render.

docs/agent-lifecycle.md

@@ -135,7 +135,9 @@ Running provider-native subagents contribute `running` to the workspace owned by
 
 ## The subagents track
 
-The collapsible track above the composer in an agent's pane (`packages/app/src/subagents/track.tsx`) combines two kinds of children:
+The track is a pill at the foot of an agent's pane (`packages/app/src/subagents/track.tsx`): a count you can read at a glance, and a panel behind it — a popover on wide screens, a sheet on compact ones — holding the rows. It floats over the transcript rather than sitting in a band above the composer, so the timeline scrolls underneath it; `packages/app/src/panels/agent-tracks.tsx` owns that placement, and the pill frame is shared with the task list in `packages/app/src/composer/tracks.tsx`.
+
+The rows combine two kinds of children:
 
 - **Paseo subagents** are full managed agents. Their membership rule (`packages/app/src/subagents/select.ts`) is:
 
@@ -165,7 +167,7 @@ Claude Code announces subagent lifecycle on the SDK stream (`task_started` / `ta
 
 Archived Paseo subagents disappear from the track, by design. To remove one from the track without closing its tab, use the **archive button** on the row — it opens a confirm dialog and archives the subagent on confirm. Provider-owned rows have no individual Paseo lifecycle controls.
 
-The track header's **Archive finished** action covers every finished row. It archives idle or errored managed Paseo subagents one at a time, and hides completed, failed, or canceled provider-owned rows in the current app session. Native sessions and timelines are untouched. Running and initializing children remain in the track. If a hidden provider child starts running again, the app brings it back to the track.
+The **Archive finished** row at the foot of the panel covers every finished row. It archives idle or errored managed Paseo subagents one at a time, and hides completed, failed, or canceled provider-owned rows in the current app session. Native sessions and timelines are untouched. Running and initializing children remain in the track. If a hidden provider child starts running again, the app brings it back to the track.
 
 To keep the agent alive but remove it from the parent's track, use **detach**. The daemon clears the relationship lifecycle labels, emits the normal agent update, and every client reclassifies the agent from subagent to root/sibling from that updated snapshot.
 
@@ -185,7 +187,7 @@ We considered universal decoupling (no tab close ever archives, archive is alway
 
 ### Subagent accumulation under long-lived parents
 
-A parent that spawns many subagents will see the track grow. Managed Paseo subagents can be archived individually or with **Archive finished**. That action hides finished provider-owned rows locally; this presentation state resets when the app restarts.
+A parent that spawns many subagents will see the panel's list grow; the pill only counts them. Managed Paseo subagents can be archived individually or with **Archive finished**. That action hides finished provider-owned rows locally; this presentation state resets when the app restarts.
 
 ### Cross-client tab dismissal
 

docs/glossary.md

@@ -42,7 +42,7 @@ Authoritative terminology. UI label wins. Don't invent synonyms; use what's here
 - **Composer toolbar** — The bottom control row inside the composer input. Contains agent controls, attachment button, voice controls, and stop/send controls. Code: `leftContent`, `beforeVoiceContent`, and `rightContent` slots in `MessageInput` (`packages/app/src/composer/input/input.tsx`). Forbidden: "Status bar".
 - **Agent controls** — Provider, model, mode, thinking, and provider-feature controls for an agent or draft agent. Code: `AgentControls` / `DraftAgentControls` (`packages/app/src/composer/agent-controls/index.tsx`). Forbidden: "Agent status bar".
 - **Composer footer** — Optional area rendered below the composer input but still inside the keyboard-shifted composer layout. Code: `Composer.footer` (`packages/app/src/composer/index.tsx`).
-- **Composer track** — A contextual lane above the composer input. Specific tracks use the `<thing> track` form: **Queue track**, **Subagents track**. Code: queue track inside `Composer` (`packages/app/src/composer/index.tsx`), `SubagentsTrack` (`packages/app/src/subagents/track.tsx`).
+- **Composer track** — A contextual lane at the foot of a pane, by the composer input. Specific tracks use the `<thing> track` form: **Queue track**, **Subagents track**, **Tasks track**. The subagents and tasks tracks are pills floating over the transcript, each opening a panel with its rows; the queue track is a lane inside the composer itself. Code: queue track inside `Composer` (`packages/app/src/composer/index.tsx`), pill and panel frame in `packages/app/src/composer/tracks.tsx`, `SubagentsTrack` (`packages/app/src/subagents/track.tsx`), `AgentTaskList` (`packages/app/src/composer/task-list/index.tsx`).
 - **Subagent** — User-facing term for an agent session related to a parent agent session. Use **subagents** in UI copy and docs. Internal daemon/provider plumbing may say "child agent" or `child_session`, especially for provider-managed imports; do not surface "child agent" as a product term.
 - **Attachment tray** — The selected-attachments row inside the composer input, above the text input. Code: `renderAttachmentTray` (`packages/app/src/composer/index.tsx`). Forbidden: "Attachment bar".
 - **Fork** — Starting a NEW agent session seeded with a copy of another session's curated chat history. The history rides along as a `chat_history` composer attachment on a draft; the fork does **not** resume or branch the provider-side session, and the source session keeps running untouched. Two targets, one surface, one RPC (`agent.fork_context`, gated on the `agentForkContext` host feature). UI: the fork menu lives in the assistant turn footer and offers "Fork in a new tab" / "Fork in a new workspace". On a **completed** turn it sits beside the copy button and pins a boundary to that turn, so the fork stops where the turn ended. On the **in-flight** turn it sits beside the progress loader and elapsed timer, and omits the boundary entirely — `selectForkContextRows` projects the whole timeline when no boundary is given, so the fork captures everything **up to now**, including the response still streaming. That omission is what makes mid-run forking work; pinning a boundary there would silently drop the live response. Forbidden on provider-subagent (read-only) panes. Code: `useForkAgent` (`packages/app/src/hooks/use-fork-agent.ts`), `selectForkContextRows` (`packages/server/src/server/agent/activity-curator.ts`). Don't confuse with: git fork (unrelated; Paseo has no such concept), **Worktree** (filesystem isolation, not history copying).