chore: enable additional lint rules for browser_tests

- no-async-promise-executor

- no-control-regex

- no-useless-rename

- no-unused-private-class-members

- unicorn/no-empty-file

Amp-Thread-ID: https://ampcode.com/threads/T-019c187a-abb8-72f9-9fe0-c1044e096770
Co-authored-by: Amp <amp@ampcode.com>

.oxlintrc.json

@@ -114,7 +114,12 @@
     {
       "files": ["browser_tests/**/*.ts"],
       "rules": {
-        "typescript/no-explicit-any": "error"
+        "typescript/no-explicit-any": "error",
+        "no-async-promise-executor": "error",
+        "no-control-regex": "error",
+        "no-useless-rename": "error",
+        "no-unused-private-class-members": "error",
+        "unicorn/no-empty-file": "error"
       }
     }
   ]