fix(omp): read omp's status bar so an omp turn can end

An omp session stayed "working" for good once a turn started, the same
latch pi had: omp's braille spinner trips the SPINNER_PATTERN fast path,
and only a composer glyph arms the idle confirmation. omp declared none,
so it fell back to Claude's `❯`, which omp never draws once its setup
wizard is done.

Measured on live omp 18.8.6 and 18.0.11 panes, holding a turn open
against a local endpoint that never answers: the input row is `╰─ <text>`
and is redrawn at submit, at the end of a turn, at launch and on
reattach. While a turn runs, the status bar's leading `π` becomes a
braille spinner plus the elapsed time (` ⠼ 14s > ⬢ model > ...`; 18.0.11
pads it with two spaces, past a minute it reads `1m`), with a
`⎋ Working…` row above it. The registry entry now names the input row as
the glyph and either working signal as the working line.

The glyph also switches the submit verifier on for omp, which reads the
input row the way it reads Claude's composer. A prompt sent mid-turn goes
to omp's Steering queue and clears the row, so the verifier stands down.
Text left in the row after an Enter is the one case it re-presses.

Verified end to end on a sandboxed instance (own HOME and PATH, omp
18.8.6): session:idle at launch, session:working during a turn,
session:idle about 3 s after it ended, and a restored pane settled idle
about 3 s after a server restart.

Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>

docs/omp-integration.md

@@ -163,9 +163,13 @@ remote user's home, so resolving locally would pin a stranger's id. See
 
 ## Known gaps
 
-- **No idle/completion hook.** Idle detection falls back to output-stabilization
-  like every other external CLI. If omp ever ships a hooks system, a Codeman hook
-  POSTing to `/api/hook-event` would be the highest-value follow-up.
+- **No idle/completion hook.** Idle detection reads the screen instead: the
+  registry entry's `workDetect` names omp's `╰─` input row as the glyph that arms
+  the idle check, and the status bar's spinner plus elapsed time (` ⠼ 14s > ⬢ …`)
+  or the `⎋ Working…` row as the working line, measured on omp 18.8.6 and 18.0.11.
+  Without it an omp session that had started a turn never left `busy`. If omp ever
+  ships a hooks system, a Codeman hook POSTing to `/api/hook-event` would still be
+  the highest-value follow-up.
 - **Killing a pane mid-turn loses the conversation for real.** `tmux kill-session`
   before an in-TUI `/exit` beats omp's own session-file flush — confirmed by direct
   testing (kill after a clean `/exit` resumes correctly; kill without `/exit` first