Type checking and other features not working with Gradle project

I used this extension to work on a Maven project originally, and it worked very well. The main features I'm interested in are type-checking (getting a warning if I call a method with bad arguments, or if I call a method that doesn't exist, say) and import warnings (being told I need to import something before using it, and being able to add the import with a single click).

Now I'm working on a Gradle project (an Android project), and these features no longer work. When I open the developer console, I see this type of error every time I open a .java file:

Error: src/main/java/com/google/android/exoplayer/demo [in demo] is not on its project's build path

Environment

• Operating System: Ubuntu 18.10
• JDK version: 1.8
• Visual Studio Code version: 1.31.1
• Java extension version: 0.39.0

まず、issue に記載された環境の詳細を使って、Gradle ベースの Android プロジェクトで Java ファイルを開いたときに報告されたエラーを再現します。プロジェクトの build path がどのように検出されるかを追跡し、動作している Maven のケースと比較します。build path のエラーなしで型チェックとインポートの警告が機能すれば完了です。