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>

test/local-echo-codex-gating.test.ts

@@ -190,7 +190,7 @@ describe('_updateLocalEchoState mode gating', () => {
     expect(app._localEchoEnabled).toBe(false);
   });
 
-  it.each(['claude', 'gemini', 'opencode'])('keeps the overlay enabled for %s sessions', (mode) => {
+  it.each(['claude', 'gemini', 'opencode', 'pi'])('keeps the overlay enabled for %s sessions', (mode) => {
     const overlay = makeOverlay();
     const app = makeApp(mode, overlay);
     app._updateLocalEchoState();
@@ -373,16 +373,19 @@ describe('_updateLocalEchoState echo policy', () => {
     expect(app._predictiveEcho.clearPredictions).toHaveBeenCalled();
   });
 
-  it.each(['claude', 'gemini', 'opencode'])("%s -> policy 'buffer' + overlay enabled (existing behavior)", (mode) => {
-    const overlay = makeOverlay();
-    const app = makeApp(mode, overlay) as PredictiveApp;
-    app._predictiveEcho = makePredictor();
-    app._updateLocalEchoState();
-    expect(app._localEchoPolicy).toBe('buffer');
-    expect(app._localEchoEnabled).toBe(true);
-    expect(overlay.prompts.length).toBeGreaterThan(0); // setPrompt still called
-    expect(app._predictiveEcho.clearPredictions).toHaveBeenCalled(); // not predict -> stray spans cleared
-  });
+  it.each(['claude', 'gemini', 'opencode', 'pi'])(
+    "%s -> policy 'buffer' + overlay enabled (existing behavior)",
+    (mode) => {
+      const overlay = makeOverlay();
+      const app = makeApp(mode, overlay) as PredictiveApp;
+      app._predictiveEcho = makePredictor();
+      app._updateLocalEchoState();
+      expect(app._localEchoPolicy).toBe('buffer');
+      expect(app._localEchoEnabled).toBe(true);
+      expect(overlay.prompts.length).toBeGreaterThan(0); // setPrompt still called
+      expect(app._predictiveEcho.clearPredictions).toHaveBeenCalled(); // not predict -> stray spans cleared
+    }
+  );
 
   it('no active session -> policy off, no crash without a predictor instance', () => {
     const app = makeApp('codex') as PredictiveApp;