fix(pi): align the doctor with the pi resolver, correct the strip rationale, update the skill

Second review pass on #282, the three items left open after f4dcfbe.

1. `codeman doctor` and the run mode disagreed about pi. The registry entry
   accepted a bare `which pi` hit while pi-cli-resolver demanded semver-shaped
   `--version` output, so the Dependencies panel could report an installed Pi CLI
   on a box where Run Pi stays hidden, which reads as a broken mode rather than a
   missing install. Both sides now share one exported PI_VERSION_REGEX, and
   PathResolver gains an opt-in `requireVersionMatch` so a binary that fails the
   shape check is reported MISSING instead of installed-with-unknown-version.
   Only pi sets it; every other tool keeps its current behaviour.

2. The isAltScreenStripMode comment justified excluding pi with "the alt screen
   is load-bearing for its fullscreen TUI". That is not what exclusion does: pi
   is tmux-backed, so it falls through to isMuxAltScreenOnlyStripMode, which
   strips the alt-screen toggles anyway. What exclusion actually preserves is
   `\x1b[3J` and the mouse DECSETs, which is the real reason (pi renders into the
   main screen and is mouse-aware). Comment and changeset now say that, and state
   the consequence: fullscreen pi paints into the main buffer, like vim in a tmux
   shell session.

3. skills/codeman still enumerated the five pre-pi modes in nine places, telling
   agents a backend does not exist and understating class-wide caveats by one
   mode. All updated, plus stale session.ts line references refreshed.

Tests: a new static guard derives the mode set from the Zod schema (not a copy)
and fails when a skill enumeration lists a partial set of external CLIs, verified
by mutation. It also documents the one legitimate exception it found: the "writes
no transcript" lists drop codex, which does write a rollout Codeman reads back.
Plus doctor cases for an unrelated `pi` on PATH and registry/resolver regex parity.

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>

skills/codeman/SKILL.md

@@ -568,7 +568,7 @@ recovered by submitting it with `{"input":"\r"}`.
 
 ⚠️ `stop` and `blocked` fire for `claude` sessions only (they are Claude Code hooks,
 and only when the workspace actually has them, see [§5.1](#51-where-to-spawn)). On
-`shell`/`opencode`/`codex`/`gemini`/`antigravity`, requesting them explicitly is a
+`shell`/`opencode`/`codex`/`gemini`/`antigravity`/`pi`, requesting them explicitly is a
 400, and lifecycle transitions there are coarse (a short shell command may emit **no**
 `idle` transition at all, verified live), so synchronize those with markers.
 
@@ -594,7 +594,8 @@ from the transcript file, which is flushed slightly *after* the `stop` hook fire
 single read taken the instant send-and-wait returns comes back `""` even though the
 turn finished (verified live: empty on the first call, full text seconds later). `text`
 is also `""` before the worker's first completed turn, and always `""` for modes with
-no transcript (`shell`, `opencode`, `gemini`, `antigravity`, verified live), which is
+no transcript (`shell`, `opencode`, `gemini`, `antigravity`, `pi`; the first four
+verified live, pi from the same source path), which is
 why the loop above is bounded rather than open-ended. Fall back to the terminal buffer
 there, tail in **bytes** (`textOutput` in `GET .../output` stays empty for interactive
 sessions; don't use it):
@@ -678,7 +679,7 @@ turn), and both better than diffing terminal samples:
 ```
 
 ⚠️ `active-tools` is parsed out of Claude's own output format, so it is **empty for
-`opencode`/`codex`/`gemini`/`antigravity`** (those parsers are skipped wholesale) and
+`opencode`/`codex`/`gemini`/`antigravity`/`pi`** (those parsers are skipped wholesale) and
 in practice empty for `shell`. Source-verified, not measured live.
 
 Only if neither helps: sample `terminal?tail=` twice a few seconds apart. A changing