Unity Animator as a scene controller

StateMachineEventReceiver.cs

using System.Collections.Generic;
using UnityEngine;
using UnityEngine.Events;
using Sirenix.OdinInspector;

// Add this to the object that holds the Animator
public class StateMachineEventReceiver : MonoBehaviour
{

    [System.Serializable]
    public class MapItem {
        public string StateName;

        [FoldoutGroup("Events")]
        public UnityEvent OnStateEnter;
        [FoldoutGroup("Events")]
        public UnityEvent OnStateUpdate;
        [FoldoutGroup("Events")]
        public UnityEvent OnStateExit;
    }

    public Animator Filter;
    public List<MapItem> Map;

    private void OnEnable() {
        StateMachineEventSource.Enter += StateMachineEventSource_OnStateEnter;
        StateMachineEventSource.Update += StateMachineEventSource_OnStateUpdate;
        StateMachineEventSource.Exit += StateMachineEventSource_OnStateExit;
    }


    private void OnDisable() {
        StateMachineEventSource.Enter -= StateMachineEventSource_OnStateEnter;
        StateMachineEventSource.Update -= StateMachineEventSource_OnStateUpdate;
        StateMachineEventSource.Exit -= StateMachineEventSource_OnStateExit;
    }


    private void StateMachineEventSource_OnStateEnter(Animator animator, AnimatorStateInfo stateInfo, int layerIndex) {
        if (Filter != null && animator != Filter) return;

        foreach (var item in Map) {
            if (stateInfo.IsName(item.StateName)) {
                item.OnStateEnter.Invoke();
                break;
            }
        }

    }

    private void StateMachineEventSource_OnStateUpdate(Animator animator, AnimatorStateInfo stateInfo, int layerIndex) {
        if (Filter != null && animator != Filter) return;

        foreach (var item in Map) {
            if (stateInfo.IsName(item.StateName)) {
                item.OnStateUpdate.Invoke();
                break;
            }
        }
    }

    private void StateMachineEventSource_OnStateExit(Animator animator, AnimatorStateInfo stateInfo, int layerIndex) {
        if (Filter != null && animator != Filter) return;

        foreach (var item in Map) {
            if (stateInfo.IsName(item.StateName)) {
                item.OnStateExit.Invoke();
                break;
            }
        }
    }
}

StateMachineEventSource.cs

using UnityEngine;

[System.Serializable]
public delegate void StateMachineStateEvent(Animator animator, AnimatorStateInfo stateInfo, int layerIndex);

// Add this to the 'root' of the Animator Controller (click on the empty space in the Animator window)
public class StateMachineEventSource : StateMachineBehaviour
{
    public static event StateMachineStateEvent Enter;
    public static event StateMachineStateEvent Update;
    public static event StateMachineStateEvent Exit;


    // OnStateEnter is called when a transition starts and the state machine starts to evaluate this state
    override public void OnStateEnter(Animator animator, AnimatorStateInfo stateInfo, int layerIndex) {
        Enter?.Invoke(animator, stateInfo, layerIndex);
    }

    // OnStateUpdate is called on each Update frame between OnStateEnter and OnStateExit callbacks
    override public void OnStateUpdate(Animator animator, AnimatorStateInfo stateInfo, int layerIndex) {
        Update?.Invoke(animator, stateInfo, layerIndex);
    }

    // OnStateExit is called when a transition ends and the state machine finishes evaluating this state
    override public void OnStateExit(Animator animator, AnimatorStateInfo stateInfo, int layerIndex) {
        Exit?.Invoke(animator, stateInfo, layerIndex);
    }
}

Odin is only used to display the list of events for Receiver in the Inspector nicely, it's not required.