feat(pi): add Pi (pi.dev) as a sixth CLI run mode (#206)

SessionMode gains 'pi', a first-class backend alongside Claude Code,
OpenCode, Codex, Gemini and Antigravity: its own PTY, tmux session, rose
tab identity, welcome button, run-mode entry, cron agentType, Docker and
remote-SSH command defaults, and clone-repo Brain option.

Pi is a different shape of CLI from the other four, and three decisions
follow from that:

- It has NO permission prompts and no sandbox, so there is no
  --dangerously-skip-permissions analog and none was invented. The
  privilege-shaped knob is the tri-state approveProjectTrust, which makes
  pi load and EXECUTE repo-local .pi/extensions TypeScript and install
  missing project packages. clampExternalCliBypassForOwner() therefore
  puts pi in the MATERIALIZE branch: a non-granted multi-user owner gets
  --no-approve even when no config was sent, because pi's own default is
  a prompt the session user could answer themselves. That helper had zero
  test coverage; it now has coverage for all four CLIs.
- Only the PI_ prefix joins the env allowlist. Pi's ~34 provider key vars
  share no prefix and ALLOWED_ENV_PREFIXES is one global list with no mode
  context, so admitting them would widen the allowlist for every mode at
  once. Auth goes through pi's /login or the server's own environment.
  --api-key is deliberately never wired: it would put a provider secret on
  the spawn command line.
- pi stays OUT of isAltScreenStripMode(). Its default TUI renders into the
  main screen with terminal-owned scrollback, and its 0.84.0 fullscreen
  mode is runtime-switchable via /settings; that flip was measured to put
  the pane into the alt screen, which the strip would have corrupted.

pi-cli-resolver.ts additionally sanity-probes `pi --version` and requires
semver-shaped output, because `pi` is a short generic name a stray binary
can shadow; GET /api/pi/status surfaces path and version so a
misresolution is diagnosable rather than presenting as a broken mode.

Docker installs pi in its own --ignore-scripts step so that flag cannot
affect the other four CLIs, and seeds its credentials per-file rather than
whole-dir (~/.pi/agent also holds sessions, extensions and package trees).

Verified end to end against pi 0.84.1 on an isolated instance: resolver
search-dir fallback, flag construction, piConfig persistence across a full
server restart, the trust prompt and its --no-approve suppression, the
rose Run button on the default daylight-blue skin (the nested skin block
eats per-mode gradients unless the rule lives inside it), and the buffer
local-echo policy, which pi tolerates where codex did not.

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

src/web/public/index.html

@@ -352,6 +352,10 @@
               <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 Gemini
             </button>
+            <button class="welcome-btn welcome-btn-pi" id="welcomePiBtn" style="display: none;" onclick="app.setRunMode('pi'); app.runPi()">
+              <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 Pi
+            </button>
           </div>
           <div class="welcome-qr" id="welcomeQr" onclick="app.toggleWelcomeQrSize()">
             <div class="welcome-qr-inner" id="welcomeQrInner"></div>
@@ -526,6 +530,9 @@
               <button class="run-mode-option" data-mode="antigravity" onclick="app.setRunMode('antigravity')">
                 <span class="run-mode-dot antigravity"></span>Antigravity
               </button>
+              <button class="run-mode-option" data-mode="pi" onclick="app.setRunMode('pi')">
+                <span class="run-mode-dot pi"></span>Pi
+              </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
@@ -801,6 +808,7 @@
                 <option value="codex">Codex</option>
                 <option value="gemini">Gemini</option>
                 <option value="antigravity">Antigravity</option>
+                <option value="pi">Pi</option>
               </select>
             </div>
             <div class="form-row"><label>Working Directory</label><input type="text" id="schWorkingDir" placeholder="/absolute/path"></div>
@@ -2481,6 +2489,7 @@
                 <option value="gemini" data-cli="gemini">Gemini</option>
                 <option value="opencode" data-cli="opencode">OpenCode</option>
                 <option value="antigravity" data-cli="antigravity">Antigravity</option>
+                <option value="pi" data-cli="pi">Pi</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>
@@ -2621,7 +2630,7 @@
             <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 + 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 + tmux.</span>
             </div>
             <div class="form-row">
               <label>Network</label>