Objects you use in every scene?

Few ideas (I'm sure there might be better ones) :

I usually have a ScriptableObject that uses SceneManager.sceneLoaded to call a delegate method whenever new scene is loaded. The "default" scripts I have stored to a prefab gameobject that is instantiated by this method. The Monobehaviours (scripts) in this Game Object are built in a Singleton pattern so they are not accidentally dublicated. They have all static self-reference so they can be easily accessed from other scripts.

I also make some components so that they will be instantiated to scene when ever they are first called. Example for this pattern: MultiTimer:Monobehaviour (Pseudocode)

         private static MultiTimer multiTimer = null;
 
         private void Awake()
         {
             this.CheckMultiTimerAvailability();
         }
 
         private void CheckMultiTimerAvailability() 
         {
             if (multiTimer == null)
             {
                 multiTimer = this;
             }
             else
             {
                 Destroy(this.gameObject);
             }
         }
 
         private static void AddTimerToSceneIfNeccessary()
         {    
             if (multiTimer == null) new GameObject("MultiTimer").AddComponent<CC_MultiTimer>();
         }
 
         public static void StartTimer(float startDelay, float duration, TimerEvent onStartCallback,  TimerEvent onEndCallback, object data = null)
         {
             MultiTimer.AddTimerToSceneIfNeccessary();
             //Do timer stuff
         }

Notice that in above pattern the static self reference is private because we want to call the actual static method (MultiTimer.StartTimer) in this class straight away to support the "first call instantiating". Reason for this pattern is that the Timer uses Coroutines cannot be static and needs to be run in a instantiated Monobehaviour.

Notice also: None of the above patterns have a persistent state over scenes. If you have any need for persistent game data then use ScriptableObjects to store them. You can, of course, make the GameObject persist over sence changes by setting it DontDestroyOnLoad. However I have (nowadays) never really needed to use that since I have used Scriptable objects for game data persistence.