Chest contents persistence between scenes

No matter what you do, you will have to store somewhere the chest contents. You can do it by storing it in the level data, or in a level database. This also means that your chest contents need to be loaded from somewhere the first time as well (or generated, but that's almost the same thing).

You could put a script onto any gameobject and add the [DontDestroyOnLoad] attribute. Have this script keep track of your chest contents, for example by having one variable for each chest (or in a collection of some sort). When loading a scene, you just find the chest and assign the contents based on your script (which is kept between scene changes).

Alternatively, as Harinezumi, save and load the data along with your level data via BinaryFormatter etc.

you can use PlayerPrefs to save your stats ,if you go to another scene or even leave the game, your stats won't change this will save your stats in registry.

for example

  using System.Collections;
  using System.Collections.Generic;
  using UnityEngine;
 public int test;

     public void Start(){
          test = PlayerPrefs.GetInt ("test");
     test += 10;
     PlayerPrefs.SetInt ("test",test);
 }

so at the first time you play this script, it will return 10,second time 20, and ....

It's just an example to give you the idea.you can check if the player picked up items and if it was true the item should not be spawned in the chest :).