This is going to be long post because of the explanation but it is really just a couple of clicks:
You could make a linked copy.
Now you have two scenes with the exact same collections.
This means that you can change something inside a collection in one scene and it will be changed inside the corresponding collection in the other scene as well.
You might want that for your lighting collection, your camera collection and your background collection but not for your collection which contains your animated objects.
For your animated object collection you want to
rightclick in outliner → duplilcate linked
You now have a new collection which contains all your animated objects. These are individual objects but all their data is shared with the original collection.
The mesh, the animation, the material and so on. This means that your file is pretty much identical and has not grown in size.
Now you want to get rid of the of the original collection.
rightclick in outliner → Unlink
Now you have two identical scenes. The only difference are the objects in your animated objects collection.
Now you go to
dope sheet → Action editor
Select the object which you want to animate differently and unlink the action it has.
Then create a new action and animate it.
The result is:
Two scenes that share everything except for the animation data of your objects.
You can also “override” the meshes of specific objects.
You can change the material but you before changing the material you have to go to the material tab and change the material from being linked to the object instead of the data.
If you want more control, performance and/or flexibility you can allways incorporate linked files, custom properties, NLA editor, geo node setups and python scripting. But for the stuff that the guy does in the video you don’t need any of that. It is really just 5 clicks or so.