test: migrate tests from centralized mjs to colocated TypeScript

Move test files from tests/ directory to colocate with source code,
convert from .mjs to .ts using tsx runner, add workspaces and npm
cache to CI workflow.

.github/workflows/test.yml

@@ -16,6 +16,10 @@ jobs:
         uses: actions/setup-node@v4
         with:
           node-version: 22
+          cache: npm
+
+      - name: Install dependencies
+        run: npm ci
 
       - name: Run tests
         run: npm test