test: add 100% coverage for apps/api and packages/types

Adds full Vitest test suites with @vitest/coverage-v8, targeting 100%
statement/branch/function/line coverage. Uses v8 ignore comments for
genuinely unreachable defensive branches.

packages/types/package.json

@@ -7,12 +7,14 @@
   "scripts": {
     "build": "tsc -p tsconfig.json",
     "lint": "eslint --max-warnings 0 src",
-    "test": "echo \"No tests for types package\""
+    "test": "vitest run --coverage"
   },
   "devDependencies": {
     "@nhcarrigan/eslint-config": "5.2.0",
     "@nhcarrigan/typescript-config": "4.0.0",
+    "@vitest/coverage-v8": "3.0.8",
     "eslint": "9.22.0",
-    "typescript": "5.8.2"
+    "typescript": "5.8.2",
+    "vitest": "3.0.8"
   }
 }