Refactor options page to use Typescript

Also, I've added and ran eslint, and fixed several minor issues accross
the Typescript codebase.

Bug: translateselectedtext:15
Change-Id: I8cfd67697f9bfb22f6de93b64fd750de66bab863
diff --git a/package.json b/package.json
index 2bda602..4ce1444 100644
--- a/package.json
+++ b/package.json
@@ -38,5 +38,10 @@
     "webpack-cli": "^4.9.2",
     "webpack-preprocessor-loader": "^1.2.0",
     "webpack-shell-plugin-next": "^2.2.2"
+  },
+  "devDependencies": {
+    "@typescript-eslint/eslint-plugin": "^5.27.0",
+    "@typescript-eslint/parser": "^5.27.0",
+    "eslint": "^8.16.0"
   }
 }