Add full test suite with unit, integration, and E2E smoke tests.

Introduce test.bat orchestrating Go/Vitest/Playwright phases, expand coverage across server, agent, and dashboard, and document in tests/README.md.

server/web/vitest.config.ts

@@ -4,5 +4,8 @@ export default defineConfig({
   test: {
     environment: 'node',
     include: ['src/**/*.test.ts'],
+    environmentMatchGlobs: [
+      ['src/api/**', 'happy-dom'],
+    ],
   },
 });