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/remote-sessions.md

@@ -1,7 +1,7 @@
 # Remote Sessions (SSH)
 
 Codeman can run a session's agent on a **remote host over SSH** instead of the
-local machine. The agent (Claude, OpenCode, Codex, Antigravity, Gemini, or a plain shell)
+local machine. The agent (Claude, OpenCode, Codex, Antigravity, Gemini, Pi, or a plain shell)
 runs inside a `tmux` server **on the remote host**, so it survives the SSH
 connection dropping; Codeman attaches to it the same way it attaches to a local
 managed session.
@@ -30,7 +30,7 @@ Types live in `src/types/session.ts`; persistence in `src/remote-hosts.ts`.
 | `RemoteHost` (extends `RemoteSshOptions`) | A saved host: `id`, `label`, `host`, `username`, `port?`, `commands?` (per-mode launch command override). |
 | `RemoteCase` | A working directory on a host: `name`, `type: 'remote'`, `hostId`, `remotePath`. |
 | `SessionRemote` (extends `RemoteSshOptions`) | The resolved bundle stamped onto a live session: host coordinates + `remotePath` + `commands`, plus **`owned?`** and **`remoteSessionName?`** (COD-105 — see [Ownership](#ownership-launched-vs-discovered-and-attached-cod-105)). Built by `toSessionRemote(host, case)` (sets `owned: true`) for the launch path, or `toAttachedSessionRemote(host, name, path)` (sets `owned: false`) for the attach path. Both copy the advanced SSH options through so every connection is identical. |
-| `RemoteCommandMode` | `Extract<SessionMode, 'shell' \| 'claude' \| 'opencode' \| 'codex' \| 'gemini' \| 'antigravity'>` — the modes that can run remotely. |
+| `RemoteCommandMode` | `Extract<SessionMode, 'shell' \| 'claude' \| 'opencode' \| 'codex' \| 'gemini' \| 'antigravity' \| 'pi'>` — the modes that can run remotely. |
 | `RemoteSessionInfo` (COD-105) | One discovered remote tmux session: `name` (always `codeman-*`), `attached` (a client is connected), `created` (epoch s), `windows`. Returned by `listRemoteCodemanSessions()`. |
 
 Persistence is two flat JSON arrays in the instance data dir: