Consider a new, informative page in Chai's documentation for working with Errors

class UntypedError {
  private readonly message;
  constructor(message: string) {
    this.message = message;
  }
}

class TypedError extends Error {
  constructor(message: string) {
    super(message);
  }
}

describe("Error Experimentation", () => {
  it("should pass in all of these cases", () => {
    // Pass
    expect(new UntypedError("untyped error no array")).to.deep.equal(new UntypedError("untyped error no array"));
    // Fail - This is the unexpected part, to me.
    expect(new TypedError("typed error no array")).to.deep.equal(new TypedError("typed error no array"));

    // This is closer to what I'm actually trying to test but is fundamentally the same thing.
    // Pass
    expect([new UntypedError("untyped error array")]).to.deep.include(new UntypedError("untyped error array"));
    // Fail - The fact that it's part of an array is probably irrelevant, but I cannot be certain.
    expect([new TypedError("typed error array")]).to.deep.include(new TypedError("typed error array"));
  });
});