Minecraft ps4 old edition although, new Minecraft has come out?

We have a world on the old version and don't want to play on the buggy new version, but he only got Minecraft yesterday and now there's no "Edition" in the main menu to change the edition.

I think that with the "Edition" change, is only possible if you have Minecraft before the big update came out. The Minecraft you buy now contains only the new Minecraft.

So I can never play with it

You can, but you have to play both on the new version.