fix(doctor): resolve CLIs via searchDirs, single-flight runs, admin-gate the group (#536 review)

- doctor probes each CLI's discovery.searchDirs when which misses and runs --version on the resolved path, so a service with a minimal PATH no longer reports installed CLIs as missing
- GET /api/doctor shares one in-flight run per category
- Diagnostics group hidden from non-admins in multi-user mode (_applyDoctorAdminGate)
- 500 uses INTERNAL_ERROR; a killed child reports 'timed out after 30 s'
- browser test blocks service workers so page.route() is reliable
- wiki: Diagnostics sentence

Co-Authored-By: Claude Sonnet 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01JrzFKEdBLwVfu6ev2ZscJS

test/doctor-settings.browser.test.ts

@@ -49,7 +49,9 @@ describe('Diagnostics panel in a real browser', () => {
     server = new WebServer(PORT, false, true);
     await server.start();
     browser = await chromium.launch({ headless: true });
-    page = await browser.newPage();
+    // A controlling service worker can swallow requests before page.route() sees them, letting the
+    // real /api/doctor (a forked Node process) answer instead; block it so the stub is reliable.
+    page = await (await browser.newContext({ serviceWorkers: 'block' })).newPage();
     await page.goto(`http://localhost:${PORT}`, { waitUntil: 'domcontentloaded' });
     await page.waitForFunction(() => (window as any).app?.terminal, null, { timeout: 30000 });
     await page.evaluate(() => (window as any).app.openAppSettings());