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/server.ts

@@ -1380,6 +1380,7 @@ export class WebServer extends EventEmitter {
         { isCodexAvailable },
         { isGeminiAvailable },
         { isAntigravityAvailable },
+        { isPiAvailable },
         { isCloudflaredAvailable },
         { isGitAvailable },
       ] = await Promise.all([
@@ -1388,6 +1389,7 @@ export class WebServer extends EventEmitter {
         import('../utils/codex-cli-resolver.js'),
         import('../utils/gemini-cli-resolver.js'),
         import('../utils/antigravity-cli-resolver.js'),
+        import('../utils/pi-cli-resolver.js'),
         import('../utils/cloudflared-resolver.js'),
         import('../git-clone.js'),
       ]);
@@ -1397,6 +1399,7 @@ export class WebServer extends EventEmitter {
         codex: isCodexAvailable(),
         gemini: isGeminiAvailable(),
         antigravity: isAntigravityAvailable(),
+        pi: isPiAvailable(),
         cloudflared: isCloudflaredAvailable(),
         // Not a run mode: the Add Case → Clone tab is an offer this box cannot
         // keep without git (issue #236), same reasoning as cloudflared above.
@@ -2634,6 +2637,7 @@ export class WebServer extends EventEmitter {
               codexConfig: muxSession.mode === 'codex' ? savedState?.codexConfig : undefined,
               geminiConfig: muxSession.mode === 'gemini' ? savedState?.geminiConfig : undefined,
               antigravityConfig: muxSession.mode === 'antigravity' ? savedState?.antigravityConfig : undefined,
+              piConfig: muxSession.mode === 'pi' ? savedState?.piConfig : undefined,
               envOverrides: savedEnvOverrides,
               effort: savedState?.effort,
               attachmentHistory: savedAttachmentHistory,