How do I shuffle a deck of cards in C#?

Have you explored the C# Random Class and its methods ? I'd like to see some code where you use that; right now it looks like you have not really done anything but write some Enums.

Let's see how simple it is to get a List of 52 unique numbers in the range #0~51:

// required in addition to the usual directives:
using System.Collections.Generic;
using System.Linq;

private Random rnd;

private List<int> ShuffledDeck;

private void ShuffleButton_Click(object sender, EventArgs e)
{
    // seed the Random with current current time millisecond value
    rnd = new Random(DateTime.Now.Millisecond);
    
    ShuffledDeck = new List<int>(52);
    
    int card;

    // create a sequence 0~51
    List<int> DeckSequence = Enumerable.Range(0, 52).ToList();

    for (int i = 0; i < 52; i++)
    {
        card = DeckSequence[rnd.Next(0, DeckSequence.Count)];
        DeckSequence.Remove(card);
        
        ShuffledDeck.Add(card);
    }
}

We create an ordered list, select a value from it with a random function, remove that selected value from the ordered list; each time we select the ordered list is getting "shorter."

Note: for a discussion of "seeding" the .NET default pseudo-random number generator: [^]. If you want better "quality" randomness, look into the "System.Security.Cryptography.RandomNumberGenerator" facility in .NET.

Enums: note that while having Enum entries with the same assigned value is "legal" in .NET, you should at least think about the issues discussed here: [^].

I recommend not to "shuffle the cards" but pick them randomly from an array initialized with all "Cards". There is no reason for real "shuffling" in a programm. But if you plan to make something connected to real Money - like online poker/blackjack platform - It's better to make it impossible for potential hackers to "see" the shuffled array. If you need the next card - just pick it randomly from the list of all cards left.