fix(pi): close four mode-list gaps in the pi run mode

Review follow-ups on #282. All four are the same failure shape: a list that
enumerates run modes, missed by the sweep that added 'pi'.

1. Cron ignored pi's project-trust clamp. The PR widened CronJobBaseSchema's
   agentType to accept 'pi' but not the matching clamp beside gemini's, so a
   non-granted multi-user owner's cron pi job spawned bare `pi` (pi's own
   defaultProjectTrust, an interactive prompt they can answer "yes" to, which
   loads and EXECUTES repo-local .pi/extensions TypeScript) while the same
   user's UI/API launch was forced to --no-approve. The clamp is now a pure
   exported helper, clampCronExternalCliConfigs(), so both it and gemini's
   previously untested materialization are pinned.

2. POST /api/sessions/:id/interactive auto-enabled the Ralph tracker for pi:
   its denylist covered opencode/codex/gemini/antigravity only. The tracker is
   never fed for an external CLI (_processExpensiveParsers returns early), so a
   pi session reported ralphEnabled and Ralph UI state no sibling backend shows.

3. REMOTE_CLI_BIN had no pi entry, so buildRemoteCliVersionProbeCommand()
   returned null and Session.cliVersion stayed blank for every remote-SSH pi
   session, even though the PR wired the remote launch command and the
   per-mode override schema field.

4. The desktop home rail's badge map had no pi entry, and its lookup falls back
   to '', which is what claude renders. A pi session read as Claude there while
   the tab strip and phone overview badged it correctly.

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

test/home-sessions.test.ts

@@ -143,6 +143,26 @@ describe('home sessions column: model', () => {
     });
     expect(plain.buildHomeSessionRows()[0].modeBadge).toBe('');
   });
+
+  it('badges every non-claude backend, so a new run mode cannot read as claude here', () => {
+    // The badge map is a per-mode lookup with a '' fallback, so a mode missing from it
+    // is indistinguishable from claude in this rail while the tab strip badges it fine.
+    for (const [mode, badge] of [
+      ['shell', 'sh'],
+      ['opencode', 'oc'],
+      ['codex', 'cx'],
+      ['gemini', 'gm'],
+      ['antigravity', 'ag'],
+      ['pi', 'pi'],
+    ] as const) {
+      const app = loadHomeSessionsApp({
+        sessions: sessionMap([{ id: 'a', mode }]),
+        sessionOrder: ['a'],
+        cases: CASES,
+      });
+      expect(app.buildHomeSessionRows()[0].modeBadge).toBe(badge);
+    }
+  });
 });
 
 describe('home sessions column: gate', () => {