fix: integration test — 24/24 pass, all subsystems operational

DoctorService:
- check_bun(): search common bun paths (~/.bun/bin/bun, /usr/*)

RuntimeApp:
- Create DatabaseHandle adapter for Bun's raw Database
- Wire migrations through proper adapter (add query() method)

Scheduler:
- rebuild_from_db(): graceful no-op when tasks table doesn't exist yet

BuiltInToolRegistrar:
- All executors return {status:'ok', ...} for ToolRegistry.call()

Integration test results: 24/24 pass
- RuntimeApp creation: 5/5 subsystems
- Startup: DB init, migrations, tools, recovery
- Tools: 10 built-in tools verified
- Tool calls: fs.read/write/list/stat, project.scan
- Shutdown: clean close

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

packages/runtime/src/doctor/DoctorService.ts

@@ -110,12 +110,20 @@ export class DoctorService {
   }
 
   private check_bun(): DoctorCheck {
-    try {
-      const version = execFileSync('bun', ['--version'], { stdio: 'pipe', timeout: 5000 }).toString().trim()
-      return { name: 'bun', category: 'self_bootstrap', passed: true, message: `Bun ${version} found`, fixable: false }
-    } catch {
-      return { name: 'bun', category: 'self_bootstrap', passed: false, message: 'Bun not found', fixable: true, fix: 'Install Bun: curl -fsSL https://bun.sh/install | bash' }
+    // Search bun in common paths, not just PATH
+    const candidates = [
+      'bun',  // PATH
+      `${process.env.HOME || '/root'}/.bun/bin/bun`,
+      '/usr/local/bin/bun',
+      '/usr/bin/bun',
+    ]
+    for (const bun of candidates) {
+      try {
+        const version = execFileSync(bun, ['--version'], { stdio: 'pipe', timeout: 5000 }).toString().trim()
+        return { name: 'bun', category: 'self_bootstrap', passed: true, message: `Bun ${version} found`, fixable: false }
+      } catch { /* try next */ }
     }
+    return { name: 'bun', category: 'self_bootstrap', passed: false, message: 'Bun not found', fixable: true, fix: 'Install Bun: curl -fsSL https://bun.sh/install | bash' }
   }
 
   private check_sqlite(): DoctorCheck {