EF Core Many To Many with owning relationship that has one

Given the following three tables what is the best way to set up the classes on the C# side along with the needed fluent configuration?

For the sake of matching my need, I will never need to get the characters by ability. Only character to abilities.

In my thinking I need to have three classes (only cause of the id on the lookup table)

abilities can be added by anyone, but no one owns them. When a character is deleted it should clean up the references in the lookup table but not delete any of it's referenced abilities. abilities can be used by any character.

I would think I need

internal class Character
{
        public virtual Guid Id { get; set; }
 
		public virtual string Name { get; set; } = string.Empty;

		public virtual ICollection<Character_Abilities> Character_Abilities{ get; set; } = new List<Character_Abilities>();
}

internal class Character_Abilities
{
        public virtual Guid Id { get; set; }

		public virtual Guid CharacterId {get;set;) = default!;

		public virtual int AbilityId { get; set; } = default!;
}

internal class Ability
{
        public virtual int Id { get; set; }

        public virtual string Name { get; set; } = string.Empty;
}

With a Fluent Config like

public DbSet<Character> Characters { get; set; } = default!;

public DbSet<Ability> Abilities { get; set; } = default!;


protected override void OnModelCreating(ModelBuilder modelBuilder)
		{
            modelBuilder.Entity<Character>(character=>
			{
			character.OwnsMany(
				t => t.AbilitiesLookup,
				char_abil=>
				{
					char_abil.HasOne<Ability>();
				});
			});

it makes sense to me as an owns many and a has one relationship as I only want to go one way. but how do I specify the entity for the middle table in the owning side? maybe I'm overthinking the relationship table. What am I missing?

In a perfect world my Character class should contain a list of Abilities; no reference to the lookup table.

Note that surrogate id is not actually required for join table and if you are not going to expose it as a separate table (i.e. public DbSet<CharacterAbility> Characters => Set<CharacterAbility>()) you can just rely on conventions to generate the table for "fully defined relationship":

public class Character
{
    public virtual Guid Id { get; set; }
 
    public virtual string Name { get; set; } = string.Empty;

    public virtual ICollection<Ability> Abilities { get; set; } = new List<Ability>();
}


public class Ability
{
    public virtual int Id { get; set; }

    public virtual string Name { get; set; } = string.Empty;

    public virtual ICollection<Character> Characters { get; set; } = new List<Character>();
}

If you want to specify the table name then you can use the fluent API to configure it:

modelBuilder
    .Entity<Character>()
    .HasMany(p => p.Abilities)
    .WithMany(p => p.Character)
    .UsingEntity(j => j.ToTable("Character_Abilities"));