Upgrade to babel@7 and support TypeScript

See https://github.com/matrix-org/matrix-react-sdk/pull/3292

Like react-sdk#3292, this fixes the couple source files which mix imports and module exports (they can't be mixed anymore).

tsconfig.json

@@ -0,0 +1,15 @@
+{
+  "compilerOptions": {
+    "target": "esnext",
+    "moduleResolution": "node",
+    "allowJs": true,
+    "noEmit": false,
+    "strict": false,
+    "isolatedModules": true,
+    "esModuleInterop": true
+  },
+  "include": [
+    "src/*.ts",
+    "src/**/*.ts"
+  ]
+}