How do I delegate my class .Equals check to a HashSet.SetEquals check?

Question

I'm having trouble getting two instances of Signature to be equal by delegating the equality check to their inner HashSet.SetEquals method, (the .Members property). I can't get a simple check to work.

SignatureMember m = new SignatureMember(typeof(int), "Test", 1);
SignatureMember b = new SignatureMember(typeof(int), "Test5", 1);

Assert.IsFalse(m == b); //Passes, as it should

Signature s = new Signature();
Signature o = new Signature();


s.Members.Add(m);
o.Members.Add(b);

Assert.IsTrue(s == o); // Fails. But using the custom comparer should mean the sets are equal.

Note the custom SignatureMemberComparer below. What am I missing?

    internal sealed class Signature:IEquatable<Signature>
    {
        public string Name { get;internal set; }

        internal HashSet<SignatureMember> Members { get; init; } = new HashSet<SignatureMember>(new SignatureMemberComparer());


        public override bool Equals(object? obj)
        {
            if (obj == null) { return false; }
            else { return Members.SetEquals(((Signature)obj).Members); }
        }

        public bool Equals(Signature? other)
        {

            if (other == null) { return false; }
            else { return Members.SetEquals(other.Members); }

        }

        public int GetHashCode([DisallowNull] Signature obj)
        {
            return Members.GetHashCode();
        }
    }

    internal class SignatureMemberComparer : IEqualityComparer<SignatureMember>
    {
        public bool Equals(SignatureMember? x, SignatureMember? y)
        {
            if(x== null & y == null) { return true; }
            else if (x != null && y != null)
            {
                return x.Type == y.Type && x.Count == y.Count;
            }
            else { throw new ArgumentOutOfRangeException(); }
        }


        public int GetHashCode([DisallowNull] SignatureMember obj)
        {
            return (obj.Type, obj.Count).GetHashCode();
        }
    }

    internal record class SignatureMember
    {
        public string Name { get; init; }
        public Type Type { get; init; }
        public int Count { get; init; }

        public SignatureMember(Type type, string name, int count)
        {
            Name = name;
            Type = type;
            Count = count;
        }

        public override int GetHashCode()
        {
            return (Name, Type, Count).GetHashCode();
        }

    }