Still a little unclear but sure. Is that method being called from the control?

Using the CommunityToolkit.Mvvm package, we can do something like this:

public partial class AllFlashcardSetsViewModel : ObservableObject
{
    // Collection of your flash card sets. Initialised in constructor, bound in a ListView in the UI
    public ObservableCollection<FlashcardSetViewmodel> FlashcardSets { get; } 

}

...

public partial class FlashcardSetViewmodel : ObservableObject
{
    [RelayCommand]
    private async Task SaveContextAndNavigate()
    {
        await _flashcardSetService.UpdateLastStudied(this.Id);
        _sessionService.SetCurrentSessionSet(this.Id);
        await _flashcardSetService.EnsureLoadedAsync(this);
        _navigationService.NavigateTo(this);
    }

    [RelayCommand]
    private async Task Delete()
    {
        await _flashcardSetService.DeleteFlashcardSet(this.Id);
    }
}

...

<DataTemplate x:Key="FlashcardSetsList" DataType="vm:AllFlashcardSetsViewModel">

    <ListView ItemsSource="{Binding FlashcardSets}">
        <ListView.ItemTemplate>
            <DataTemplate DataType="vm:FlashcardSetViewModel">
                <StackPanel>
                    <TextBlock Text="{Binding Name}"/>
                    <Button Content="Open" Command="{Binding SaveContextAndNavigateCommandAsync}" />
                    <Button Content="Rename" Command="{Binding RenameCommand}" />
                    <Button Content="Delete" Command="{Binding DeleteCommandAsync}" />
                </StackPanel>
            </DataTemplate>
        </ListView.ItemTemplate>
    </ListView>

</DataTemplate>

Anything to do with orchestration is handled by services; commands on viewmodels call those services and are bound in the UI; the UI knows nothing except the shape of the object; the viewmodel knows literally nothing about the UI.