I am currently digging through the Android Room with a View sample app, full source code available here. In this project, an WordViewModel of type Android
AndroidX-Activity 1.2.0's ComponentActivity (and therefore AppCompatActivity) implements HasDefaultViewModelProviderFactory, which returns an ViewModelProvider.AndroidViewModelFactory.getInstance(getApplication()) from your Activity/Fragment by default, allowing you to get the application from this AndroidViewModelFactory without you having to explicitly pass it.
Then, this factory instantiates your ViewModel via reflection using a __(application) constructor.
It's generally a better idea to use SavedStateViewModelFactory in order to be able to receive a SavedStateHandle in a similar manner (___(application, savedStateHandle)) though.
So to fix the problem, you need to add up-to-date versions of core-ktx, activity-ktx and fragment-ktx explicitly in your code.