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/cron-service.test.ts

@@ -16,7 +16,7 @@ import { describe, it, expect, beforeEach, vi } from 'vitest';
 import { existsSync, mkdtempSync, mkdirSync, writeFileSync, symlinkSync } from 'node:fs';
 import { tmpdir } from 'node:os';
 import { join } from 'node:path';
-import { CronService, type CronDeps } from '../src/cron/cron-service.js';
+import { CronService, clampCronExternalCliConfigs, type CronDeps } from '../src/cron/cron-service.js';
 import { CronJobSchema } from '../src/web/schemas.js';
 import { MAX_CRON_JOBS } from '../src/config/map-limits.js';
 import type { CronJob, CronJobRun } from '../src/types/cron.js';
@@ -632,3 +632,36 @@ describe('CronService', () => {
     });
   });
 });
+
+/**
+ * The §6.3 clamp cron applies at FIRE time. Cron sends no per-CLI config, so a
+ * missing clamp here is not "the default applies" but "the CLI's own unsafe default
+ * applies", which is the whole reason gemini and pi are materialized rather than
+ * left absent like codex/antigravity.
+ */
+describe('clampCronExternalCliConfigs', () => {
+  it('leaves everything undefined for a granted owner (upstream defaults)', () => {
+    expect(clampCronExternalCliConfigs('gemini', true)).toEqual({ geminiConfig: undefined, piConfig: undefined });
+    expect(clampCronExternalCliConfigs('pi', true)).toEqual({ geminiConfig: undefined, piConfig: undefined });
+  });
+
+  it('materializes gemini auto_edit for a non-granted owner (its default is yolo)', () => {
+    expect(clampCronExternalCliConfigs('gemini', false)).toEqual({
+      geminiConfig: { approvalMode: 'auto_edit' },
+      piConfig: undefined,
+    });
+  });
+
+  it('materializes pi --no-approve for a non-granted owner (its default is an answerable prompt)', () => {
+    expect(clampCronExternalCliConfigs('pi', false)).toEqual({
+      geminiConfig: undefined,
+      piConfig: { approveProjectTrust: false },
+    });
+  });
+
+  it('clamps nothing for modes whose absent config already spawns safe', () => {
+    for (const mode of ['claude', 'shell', 'opencode', 'codex', 'antigravity'] as const) {
+      expect(clampCronExternalCliConfigs(mode, false)).toEqual({ geminiConfig: undefined, piConfig: undefined });
+    }
+  });
+});