feat(approvals): let a watching session keep quiet, and fix the tui gate

The badge alone left the row in NEEDS YOU, which is the thing the issue was
about. The fix is the alert that does not fire.

An idle prompt from a session that is watching its own background work now
opens ALREADY acknowledged. `hook-event-routes` passes `Session.watching` to
`notePrompt()`, which sets `acknowledgedAt` and records why in a new
`acknowledgedReason`. Nothing new suppresses anything: `acknowledge()` has
always meant "the alert this prompt armed is spent", and the prompt itself
stays pending, answerable and available as Read My Mind context. A wrong label
therefore costs a card that does not blink, never an alert that was never
created.

Every surface follows from that. The broadcast carries the reason, so a live
page declines to arm the tab alert and raises no desktop notification. The push
is skipped, since a false alarm is hardest to ignore on a phone. A reloading
page reads `acknowledgedAt` in `seedApprovals()`, which it already did. And
`classifySession()` now reads it too, which is a pre-existing bug fixed here:
acknowledging on one device cleared the alert everywhere except `codeman tui`.
It re-arms for free, because the next idle prompt supersedes the item and is
built fresh. Only `idle` is eligible, so a dialog that blocks the agent still
goes red whatever else it started.

The label is pane-derived and therefore prompt-injectable, so it is now read
from the last two rows of the screen only, with Claude's pattern anchored on
the `·` its footer joins items with, ANSI-stripped and length-capped at the
source. An agent that prints `· 1 monitor ·` into its own output finds no
match.

Verified on an isolated beta: a session that armed a monitor took its idle
prompt acknowledged with no alert on any surface, wore the badge, and showed
"quiet, watching 1 monitor" on its still-answerable card; the same session with
the monitor killed alerted normally on the next prompt. `test/watching-no-alert.test.ts`
pins both directions across all four surfaces.

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>

.changeset/watching-badge.md

@@ -2,4 +2,12 @@
 'aicodeman': minor
 ---
 
-Sessions now say when they are watching work they started themselves. An agent that arms a monitor, backgrounds a shell or hands a task to a cloud session is told to end its turn, so the pane goes quiet, Claude Code's idle notification lands a minute later and the session shows up under NEEDS YOU with nothing for anyone to answer. Claude prints what it is still running on the last row of its screen, and the CLI registry now carries that row as `capabilities.workDetect.watchingLine`, so the idle probe reads the label ("1 monitor", "2 shells") along with the working line it already reads. The label reaches every session payload as `watching`, and the phone overview, the desktop home rail and the rich sidebar rows wear it as a `watching` badge in the accent colour. It sits beside the state pill and never replaces it, because an agent can arm a monitor and ask you a question in the same breath.
+A session watching work it started itself no longer asks you to look at it. An agent that arms a monitor, backgrounds a shell or hands a task to a cloud session is told to end its turn, so the pane goes quiet, Claude Code's idle notification lands a minute later, and the session shows up under NEEDS YOU with nothing for anyone to answer.
+
+Claude prints what it is still running on the last row of its screen, and the CLI registry now carries that row as an optional `capabilities.workDetect.watchingLine`. The idle probe reads the label ("1 monitor", "2 shells") off the capture it already takes when a turn ends, and it reaches the session payload as `watching`.
+
+The prompt that follows then opens already acknowledged. It stays in the Approvals drawer, stays answerable and stays Read My Mind context, and only the alert it would have armed is spent: no tab alert, no desktop notification, no push, and no NEEDS YOU row on any surface, `codeman tui` included. The card says why, reading "quiet, watching 1 monitor" rather than implying somebody looked. It re-arms by itself, because the next idle prompt supersedes this item and is built fresh. A permission or question dialog still goes red whatever else the agent started.
+
+Sessions also wear a `watching` badge beside their state pill on the phone overview, the desktop home rail and the rich sidebar and rail rows.
+
+Fixes a pre-existing bug in the same gate: `classifySession()` never looked at `acknowledgedAt`, so an idle alert cleared by opening the session on another device stayed lit in `codeman tui` alone.