I am following this ionic tutorial and having some trouble with setting up the SDK in Android Studio in order to test my ionic project. I am looking for the SDK manager however
You have accidently disabled Android Support plugin in your plugin list. Try enable it and restart Android Studio.
To be detailed: In your first picture, Configure -> Plugins, tick almost everything to enable (for me which is also using Android Studio 3.1.3, there are Android Support, Android APK Support, Firebase Services, Google Developers Samples, Firebase App Indexing, Firebase Testing, Test Recorder, Google Services, Google Cloud Tools For Android Studio, Android NDK Support, Android Games and App Links Assistant), then OK to Restart Android Studio.