There is literally no way to view your reading list or remove entries. All you can do is click the icon to add articles to the default list.
That isn't helpful at all! Why does this even exist? Just another Wikimedia Foundation project that nobody asked for.
Do they really expect users to add entries on PC and then open the app on your phone to view or delete entries?
You already implemented the sync feature, which is far more complicated. So, why don't you go all the way and add editing and viewing to the browser extension?