feat(deepseek): add DeepSeek Harness (dsh) as a ninth CLI run mode

Adds `mode: 'deepseek'` alongside claude/shell/opencode/codex/gemini/
antigravity/pi/grok, plus a shortcut that opens the harness's own browser UI
as a Codeman web tab.

DeepSeek is wired unlike its siblings in three ways, each of which is the
reason for a design decision rather than an accident:

1. The agent is a PROFILE, not the binary. `dsh` is a launcher over
   $DSH_HOME/profiles/<name>, and DeepSeek ships only `web`, `headless` and
   `base` -- the interactive terminal front door is always a third-party
   plugin. So availability is two questions: `isDeepSeekAvailable()` (binary)
   and `isDeepSeekRunnable()` (binary AND a pane-capable profile). The Run
   button gates on the latter, because reporting only the binary would spawn a
   pane that dies on arrival. When the binary is present but no profile is,
   the run menu offers to install one (POST /api/deepseek/install-profile).

2. The permission switch is an env var, not a flag. The harness has no
   command-line permission option; its sandbox/approval rows read
   DSH_PERMISSION_MODE (read-only / workspace-write / danger-full-access).
   Exported via `tmux setenv`, never on the spawn line. Absent = the harness's
   own workspace-write, which still asks, so the multi-user clamp is the
   only-if-sent branch and clamps to workspace-write, never read-only.

3. It is the only non-claude mode that passes hooksAvailableForMode(), and it
   earned that. The terminal front door reports idle/working/blocked to a
   supervising process over a generic env-gated contract; a generated shim
   (deepseek-status-shim.ts) makes Codeman that supervisor and forwards each
   report to /api/hook-event as stop / agent_working / permission_prompt. So a
   dsh session gets definitive respawn triggers, real wait-endpoint signals and
   real Approvals Inbox items instead of output-stabilization guesswork.
   `agent_working` is new (157th SSE constant) and joins
   APPROVAL_RESOLVING_EVENTS so a dialog answered in the terminal clears its
   alert at once.

The resolver needs the strictest identity probe of the family: `dsh` is not
merely a squattable npm name, Debian ships an unrelated `dsh` (dancer's shell),
so `dsh --help` must print the harness's own banner before a candidate is
handed a spawn line.

Model is deliberately not a session field -- it is a composition entry in the
profile's config tree. Env allowlist gains DSH_* and DEEPSEEK_* only; provider
keys named by a settings-file `apiKeyEnv` stay out, which is pi's
34-provider-key problem in a new shape.

Verified live against dsh 0.1.1-rc.2 and @deepseek-harness-tui/dsh-tui: the
status endpoint's two-part answer, the no-profile refusal, the profile
bootstrap, a real session whose pane runs `dsh --profile dsh-tui` with the
permission mode injected via setenv, and the full status bridge -- a
send-and-wait returned signal "stop" from a real turn, and blocked/working
created and cleared an Approvals Inbox item.

Docs: docs/deepseek-integration.md (guide), docs/deepseek-integration-plan.md
(decisions + honest gaps). Tests: test/deepseek-mode.test.ts,
test/deepseek-cli-resolver.test.ts.

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

src/web/public/index.html

@@ -448,6 +448,10 @@
               <svg width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2"><polygon points="5 3 19 12 5 21 5 3"/></svg>
               Run Grok
             </button>
+            <button class="welcome-btn welcome-btn-deepseek" id="welcomeDeepSeekBtn" style="display: none;" onclick="app.setRunMode('deepseek'); app.runDeepSeek()">
+              <svg width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2"><polygon points="5 3 19 12 5 21 5 3"/></svg>
+              Run DeepSeek
+            </button>
           </div>
           <div class="welcome-qr" id="welcomeQr" onclick="app.toggleWelcomeQrSize()">
             <div class="welcome-qr-inner" id="welcomeQrInner"></div>
@@ -630,6 +634,15 @@
               <button class="run-mode-option" data-mode="grok" onclick="app.setRunMode('grok')">
                 <span class="run-mode-dot grok"></span>Grok
               </button>
+              <button class="run-mode-option" data-mode="deepseek" onclick="app.setRunMode('deepseek')">
+                <span class="run-mode-dot deepseek"></span>DeepSeek
+              </button>
+              <!-- Shown only when `dsh` is installed but no pane-capable profile is:
+                   DeepSeek ships no terminal front door, so the fix is an install,
+                   not a greyed-out entry the user cannot act on. -->
+              <button class="run-mode-option run-mode-option-install" data-action="deepseek-install" id="runModeDeepSeekInstall" style="display: none;" onclick="app.installDeepSeekProfile()">
+                <span class="run-mode-dot deepseek"></span>DeepSeek — add a terminal profile…
+              </button>
               <div class="run-mode-sep"></div>
               <button class="run-mode-option" data-mode="shell" onclick="app.setRunMode('shell')">
                 <span class="run-mode-dot shell"></span>Terminal / Shell
@@ -642,6 +655,13 @@
               <button class="run-mode-option run-mode-option--add" onclick="app.showWebviewModal()">
                 <span class="run-mode-dot web"></span>Add URL&hellip;
               </button>
+              <!-- The DeepSeek Harness browser UI is the vendor's OWN interactive
+                   surface (the terminal one is third-party), so it gets a shortcut:
+                   this starts `dsh web` in a shell session and opens it as a tab.
+                   Shown only when dsh is installed. -->
+              <button class="run-mode-option run-mode-option--web" id="runModeDeepSeekWeb" style="display: none;" onclick="app.runDeepSeekWeb()">
+                <span class="run-mode-dot deepseek"></span>DeepSeek web UI&hellip;
+              </button>
               <div class="run-mode-sep"></div>
               <div class="run-mode-header">Recent Sessions</div>
               <div class="run-mode-history" id="runModeHistory"></div>
@@ -908,6 +928,7 @@
                 <option value="antigravity">Antigravity</option>
                 <option value="pi">Pi</option>
                 <option value="grok">Grok</option>
+                <option value="deepseek">DeepSeek</option>
               </select>
             </div>
             <div class="form-row"><label>Working Directory</label><input type="text" id="schWorkingDir" placeholder="/absolute/path"></div>
@@ -2676,6 +2697,7 @@
                 <option value="antigravity" data-cli="antigravity">Antigravity</option>
                 <option value="pi" data-cli="pi">Pi</option>
                 <option value="grok" data-cli="grok">Grok</option>
+                <option value="deepseek" data-cli="deepseek">DeepSeek</option>
                 <option value="shell">Shell (no agent)</option>
               </select>
               <span class="form-hint">Which CLI to point the Run button at once the clone finishes. Changeable any time from the Run dropdown.</span>
@@ -2816,7 +2838,7 @@
             <div class="form-row">
               <label>Image</label>
               <input type="text" id="dockerImage" placeholder="codeman/agent:base" autocomplete="off" autocapitalize="off" spellcheck="false">
-              <span class="form-hint">Build it once with <code>node scripts/build-agent-image.mjs</code>. Contains node + claude/codex/gemini/opencode/agy/pi/grok + tmux.</span>
+              <span class="form-hint">Build it once with <code>node scripts/build-agent-image.mjs</code>. Contains node + claude/codex/gemini/opencode/agy/pi/grok/dsh + tmux.</span>
             </div>
             <div class="form-row">
               <label>Network</label>