demo.cs

using System;
using System.Reflection;

public class SomeType
{
    static void Main() => new SomeType().DoTheThing();
    public void DoTheThing()
    {
        var prop = GetType().GetProperty(nameof(AgreedInstallationDate));
        var value = new DateTime(2021, 08, 17);
        UpdateProperty(prop, value);
    }
    public DateTime? AgreedInstallationDate { get; set; }
    private void UpdateProperty(PropertyInfo prop, object newValue)
    {
        // Align data type
        Type propType = prop.PropertyType;

        if (propType.IsGenericType && propType.GetGenericTypeDefinition() == typeof(Nullable<>))
        {
            newValue = ChangeTypeEx(newValue, propType);
        }

        // Store changes back to entity
        prop.SetValue(this, newValue);

        // Even this doesn't work
        prop.SetValue(this, (DateTime?)DateTime.Now);
    }

    public static object ChangeTypeEx(object obj, Type type)
    {
        Type targetType = Nullable.GetUnderlyingType(type) ?? type;

        if (obj == null)
        {
            System.Reflection.ConstructorInfo defaultConstructor = targetType.GetConstructor(Type.EmptyTypes);

            return defaultConstructor?.Invoke(new object[0]) ?? obj;
        }

        return Convert.ChangeType(obj, targetType);
    }
}