Do I really need a static class to manage favorites?

Hi have a conception problem. I work on a pro app to calculate some scores. I do it with C# / Xamarin.Forms. I want to manage favorites, so that the user can have a limited score list to find its favorites faster.

I have 4 tabs :

1. Entire score list ==> navigates to chosen score
2. Favorites list ==> navigates too
3. & 4. : not a problem here

So I want that when the user adds/deletes a score from the favorites list, this is changed in the first and the second tab. For the moment I have this :

public static class FavoritesManager
{
    public static ObservableCollection<string> FavoritesList = new ObservableCollection<string>();

    // Indexer does not work because static class ==> this is one of the problems
    // public bool this[string key] { get => this.Favs.Contains(key); }
}

// My ViewModel
public class ScoreListViewModel : ViewModelBase
{
    // Each Category is a List<Score>. Score has 3 properties : string Title, string Detail, bool IsFavorite
    public ObservableCollection<Category> Categories { get; set; }

    public ScoreListViewModel()
    {
        this.InitializeCategories();

        FavoritesManager.FavoritesList.CollectionChanged += OnFavoritesChanged;
    }

    // When favorites list has changed ==> event CollectionChanged
    public void OnFavoritesChanged(object sender, NotifyCollectionChangedEventArgs e)
    {
        this.InitializeCategories();
    }

    public void InitializeCategories()
    {
        this.Categories = new ObservableCollection<Category>
        {
            new Category ("Cat1")
            {
                new Score("Foo", "Bar", FavoritesManager.FavoritesList.Contains("Foo"))
            }
        };
    }

    // Command used to add a favorite
    public ICommand AddToFavorites => new Command<string>((fav) =>
    {
        FavoritesManager.FavoritesList.Add(fav);
    });
}

So I have 2 questions :

1. How to avoid dependency of ViewModel to the static class FavoritesManager ? Do I really need a static class or is there another way to "share" it in real time through different views ? Because if I decide to change favorites management, when I will have 30-40 scores in the list, it will be very difficult...

2. Is there a way to avoid complete reinitialization of the Categories list each time I change just 1 thing (1 favorite) ? This is, I think, mostly a XAML / Binding question...

Thanks for your help, Galactose