Expand test coverage across server, agent, and web; fix bugs found during audit.

Adds hundreds of unit/integration/e2e tests, fixes WS bcrypt auth, config merge, fleet analytics, agent schedule/log tail, and documents stale PROBLEMS items. Updates PROBLEMS.md, README, and test scripts; ignores local spread-kits and coverage dirs.

server/web/vitest.config.ts

@@ -11,6 +11,7 @@ export default defineConfig({
       ['src/hooks/**', 'happy-dom'],
       ['src/pages/**', 'happy-dom'],
       ['src/components/**', 'happy-dom'],
+      ['src/App.test.tsx', 'happy-dom'],
     ],
   },
 });