fix: include type augmentation files in browser_tests tsconfig

- Add src/types/**/*.d.ts and global.d.ts to include array

- Use vue-tsc for typecheck:browser to match main typecheck

- Fixes ~160 src/ type errors in browser test compilation

Amp-Thread-ID: https://ampcode.com/threads/T-019c16af-3867-74d9-9242-e3fa8e17947e
Co-authored-by: Amp <amp@ampcode.com>

browser_tests/tsconfig.json

@@ -7,5 +7,5 @@
     "noUnusedParameters": true,
     "resolveJsonModule": true
   },
-  "include": ["**/*.ts"]
+  "include": ["**/*.ts", "../src/types/**/*.d.ts", "../global.d.ts"]
 }