docs(wiki): catch the manual up to 1.29.0 and add the three run modes it never had

The wiki was written for seven run modes and never received Grok Build, DeepSeek
Harness or OMP. They now appear everywhere the others do: the modes table and
per-CLI notes, install commands, environment prefixes, the Quick Start table, the
requirements rows, the vocabulary, and every "seven modes" count.

The 1.27 to 1.29.0 changes land on the pages that own them: attaching a case to an
existing container, multi-case adoption and the copy-a-case picker (Docker Cases);
file reads over ssh in remote cases and what stays unavailable (Remote SSH Sessions,
Working With Files, Security); single-page app routing, frame recovery, localhost
links as tabs and the egress guard (Web Tabs); DeepSeek as the one non-Claude mode
with real stop/blocked signals and Approvals items, Codex's own work detection,
last-response, the model-endpoint routes and refreshed counts (HTTP API, Driving
From An Agent, Hooks, Notifications, Keeping Agents Running, Core Concepts);
Shift+drag, right-click copy, Auto Copy, the Ctrl+Z guard, font weight, the vertical
rail and its activity sort (Keyboard Shortcuts, Input And Voice, The Dashboard,
Settings Reference); the 600px phone cutoff, Codex shift arrows and iPhone Duo
(Mobile Guide); the Docker Compose route and its update rule (Installation, Running
As A Service); four new symptom entries and a "which CLIs" question (Troubleshooting,
FAQ).

Custom model endpoints are deliberately left to #430, which adds that page and edits
Agent CLIs, Settings Reference and the sidebar; these edits stay out of the regions
#430, #428 and #376 touch, and all three still merge cleanly on top.

Both READMEs: the web-tab menu entry is labelled "Add URL" in the UI, not
"Add dashboard".

Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com>

docs/wiki/Driving-Codeman-From-An-Agent.md

@@ -54,7 +54,10 @@ create-time sweep would yank the skill out from under other live sessions sharin
 directory. Remove them per case with `codeman skill uninstall --case <name>`.
 
 The skill ships with the verb index always loaded, plus on-demand references for the verbs,
-worked multi-worker recipes, endpoint tables, and cross-session messaging.
+worked multi-worker recipes, endpoint tables, and cross-session messaging. It drives
+DeepSeek Harness workers the same way it drives Claude ones (`spawn_workers alpha
+beta:deepseek` is a mixed fleet in one call), since those are the two modes with real
+completion signals.
 
 ## The manual path
 
@@ -92,8 +95,9 @@ Read these before writing any code. Each one has cost somebody an afternoon.
 5. **Wait instead of polling, and a timeout is not an error.** The wait endpoints answer
    `200` with `wait.timedOut: true`. Loop over short waits rather than one long call, because
    tunnels cut idle connections.
-6. **Only `claude` sessions emit `stop` and `blocked`.** They come from Claude Code hooks.
-   Shell and the external CLIs accept only `idle`, `working`, and `exit`; asking for `stop`
+6. **Only `claude` and `deepseek` sessions emit `stop` and `blocked`.** Claude's come from
+   Claude Code hooks, DeepSeek's from the harness reporting its state to Codeman. Shell and
+   the other external CLIs accept only `idle`, `working`, and `exit`; asking for `stop`
    explicitly there is a `400`, while omitting `until` is always safe. On a shell session
    `idle` fires **once at startup and never again**, so synchronize hook-less sessions with an
    output marker instead.
@@ -130,7 +134,10 @@ curl -s -X POST "$API/api/sessions/$ID/input" \
 # Or wait for a marker in the output, which works on shell sessions too
 curl -s "$API/api/sessions/$ID/wait-output?contains=DONE_17909&from=buffer" | jq
 
-# Read the terminal back
+# Read the last answer as clean text (claude, codex, deepseek sessions)
+curl -s "$API/api/sessions/$ID/last-response" | jq -r '.data.text'
+
+# Or read the terminal back
 curl -s "$API/api/sessions/$ID/terminal?tail=4000" | jq -r '.data.output'
 
 # Clean up, by exact id
@@ -157,7 +164,13 @@ Make it unique per call, because tmux repaints replay old screen text.
 
 ### Reading output
 
-Use `terminal?tail=`, not `/output`. The latter's text field is empty for every tmux-backed
+For `claude`, `codex` and `deepseek` sessions, read the answer from the transcript rather
+than the screen: `GET /api/sessions/:id/last-response` returns the last reply as clean text
+with no TUI frames or repaint noise. Poll it briefly rather than reading once, because the
+transcript lands slightly after the `stop` signal, so a read immediately after send-and-wait
+returns often comes back empty.
+
+For everything else, use `terminal?tail=`, not `/output`. The latter's text field is empty for every tmux-backed
 session, which is every interactive session. `tail` counts **bytes**, and what comes back is
 terminal data with ANSI sequences included.