Upgrade our eslint config to the latest (#24647)

* Fix lint error in test-utils.ts

* Upgrade eslint config (and separate projects to support it)

* Handle possibility that req.error could be null

.eslintrc.js

@@ -1,6 +1,9 @@
 module.exports = {
     plugins: ["matrix-org"],
     extends: ["plugin:matrix-org/babel", "plugin:matrix-org/react"],
+    parserOptions: {
+        project: ["./tsconfig.json"],
+    },
     env: {
         browser: true,
         node: true,
@@ -16,7 +19,7 @@ module.exports = {
     },
     overrides: [
         {
-            files: ["src/**/*.{ts,tsx}", "test/**/*.{ts,tsx}", "module_system/**/*.{ts,tsx}"],
+            files: ["src/**/*.{ts,tsx}", "test/**/*.{ts,tsx}"],
             extends: ["plugin:matrix-org/typescript", "plugin:matrix-org/react"],
             // NOTE: These rules are frozen and new rules should not be added here.
             // New changes belong in https://github.com/matrix-org/eslint-plugin-matrix-org/