Set up unit testing infrastructure

- Extract slot generation logic into apps/api/src/lib/slots.ts for testability
- Add 8 unit tests covering slot generation edge cases (overlap, multi-groomer, boundary)
- Add @testing-library/react + jsdom to apps/web; configure vitest with jsdom environment
- Add 4 component tests for App navigation rendering and active-link highlighting
- Remove passWithNoTests: true from both vitest configs; add coverage thresholds

Closes #39

Co-Authored-By: Paperclip <noreply@paperclip.ing>

apps/api/vitest.config.ts

@@ -2,6 +2,13 @@ import { defineConfig } from "vitest/config";
 
 export default defineConfig({
   test: {
-    passWithNoTests: true,
+    coverage: {
+      provider: "v8",
+      include: ["src/lib/**"],
+      thresholds: {
+        lines: 80,
+        functions: 80,
+      },
+    },
   },
 });