Input.anyKey still detecting mouse input after implementing workaround

I am trying to make sure my game does not start on mouse click, and only on the press of a key, but the workaround seen below that I implemented does not seem to have worked. Any ideas on how to fix this?

using System.Collections;
using System.Collections.Generic;
using UnityEngine;
using UnityEngine.SceneManagement;

public class ChangeScene : MonoBehaviour
{
    private bool soundPlaying;
    public GameObject BackgroundSound;
    public AudioSource start;

    void Start() {
        BackgroundSound.SetActive(true);
    }

    void Update() {
        if (Input.anyKey) {
            if (Input.GetMouseButtonDown(0) || Input.GetMouseButtonDown(1) || Input.GetMouseButtonDown(2)) {
                Debug.Log("done");
                return;
            }
            else
            {
                BackgroundSound.SetActive(false);
                start.Play(0);
                soundPlaying = true;
            }
        }
        if (!start.isPlaying && soundPlaying) {
                SceneManager.LoadScene("HowToPlay");
        }
    }
}

Test for GetMouseButton, instead of GetMouseButtonDown and you’ll be fine…

    void Update()
    {
        if (Input.anyKey)
        {
            if (Input.GetMouseButton(0) || Input.GetMouseButton(1) || Input.GetMouseButton(2))
            {
                print("Mouse Button");
            }
            else
            {
                print("Not Mouse Button");
            }
        }
    }