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>

docs/cron-guide.md

@@ -91,7 +91,7 @@ These map 1:1 to `CronJobSchema` (`src/web/schemas.ts`) and the `CronJob` type
 | Field                      | Required    | Values / limits                                          | Notes                                                                                                                                                                                      |
 | -------------------------- | ----------- | -------------------------------------------------------- | ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ |
 | `name`                     | ✅          | 1–200 chars                                              | Display name; also used as the created session's name.                                                                                                                                     |
-| `agentType`                | ✅          | `claude` \| `shell` \| `opencode` \| `codex` \| `gemini` \| `antigravity` | Reuses Codeman's `SessionMode`. `shell` = a plain terminal.                                                                                                                                |
+| `agentType`                | ✅          | `claude` \| `shell` \| `opencode` \| `codex` \| `gemini` \| `antigravity` \| `pi` | Reuses Codeman's `SessionMode`. `shell` = a plain terminal. ⚠️ A `pi` job's readiness poll looks for `❯`/a token count, neither of which pi prints, so it burns the poll budget and then sends the prompt anyway (slower start, still works). |
 | `workingDir`               | ✅          | valid path (allowlist-validated)                         | Validated at **create/update** (must exist, be a directory, and not resolve into a blocked tree — `/etc`, `/root`, `/proc`, `/sys`, `/dev`, or `/` itself) and again **at fire time**.     |
 | `launchCommand`            | —           | ≤ 2000 chars, single line                                | `shell` mode only: sent as the **first input line** once the shell is up, before the prompt. Ignored for other agent types.                                                                |
 | `promptMode`               | ✅          | `inline_text` \| `prompt_file_path`                      | See §5.                                                                                                                                                                                    |