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/app.js

@@ -2003,9 +2003,11 @@ class CodemanApp {
         ? 'Gemini'
         : mode === 'antigravity'
           ? 'Antigravity'
-          : mode === 'opencode'
-            ? 'OpenCode'
-            : 'Claude';
+          : mode === 'pi'
+            ? 'Pi'
+            : mode === 'opencode'
+              ? 'OpenCode'
+              : 'Claude';
   }
 
   async toggleResponseViewer() {
@@ -3881,7 +3883,7 @@ class CodemanApp {
           <span class="tab-status ${status}" aria-hidden="true"></span>
           <span class="tab-info">
             <span class="tab-name-row">
-              ${mode === 'shell' ? '<span class="tab-mode shell" aria-hidden="true">sh</span>' : mode === 'opencode' ? '<span class="tab-mode opencode" aria-hidden="true">oc</span>' : mode === 'codex' ? '<span class="tab-mode codex" aria-hidden="true">cx</span>' : mode === 'gemini' ? '<span class="tab-mode gemini" aria-hidden="true">gm</span>' : mode === 'antigravity' ? '<span class="tab-mode antigravity" aria-hidden="true">ag</span>' : ''}
+              ${mode === 'shell' ? '<span class="tab-mode shell" aria-hidden="true">sh</span>' : mode === 'opencode' ? '<span class="tab-mode opencode" aria-hidden="true">oc</span>' : mode === 'codex' ? '<span class="tab-mode codex" aria-hidden="true">cx</span>' : mode === 'gemini' ? '<span class="tab-mode gemini" aria-hidden="true">gm</span>' : mode === 'antigravity' ? '<span class="tab-mode antigravity" aria-hidden="true">ag</span>' : mode === 'pi' ? '<span class="tab-mode pi" aria-hidden="true">pi</span>' : ''}
               <span class="tab-name" data-session-id="${id}">${escapeHtml(tabLabel)}</span>
               <span class="tab-detached-badge" aria-hidden="true">detached</span>
             </span>
@@ -5053,7 +5055,9 @@ class CodemanApp {
             ? 'Kill Tmux & Gemini'
             : session.mode === 'antigravity'
               ? 'Kill Tmux & Antigravity'
-              : 'Kill Tmux & Claude Code';
+              : session.mode === 'pi'
+                ? 'Kill Tmux & Pi'
+                : 'Kill Tmux & Claude Code';
     }
 
     document.getElementById('closeConfirmModal').classList.add('active');