Minecraft world saves can be transferred from one system to another, although you need a flash drive in order to do so.
Before doing anything, make sure to put everything that was in your inventory into a chest, and then make sure to save and quit the game. THIS IS IMPORTANT SO THAT YOU DEFINITELY KEEP YOUR INVENTORY.
You need to then take a formatted USB flash drive, and connect it to your PS4, and sign in to the account that has the worlds on it. You then need to go to your home page, and then go to settings > storage > (select whatever storage device you know Minecraft is downloaded on, either extended storage* or system storage) > Minecraft > "Transfer game data to USB storage device"** > and then select your world save file. After it is done, you can then log out, and then either remove the USB flash drive, or keep it in. Make sure that the Flash drive is inserted into the device that you want the worlds on, and then follow the same chain of menus, instead, select "Transfer game data from storage device"**. Then, after it is done, restart your PS4, and then boot up Minecraft. You should then see the save file that you selected. I am not entirely sure if this keeps your inventory or not, but you have everything else.
- *If applicable
- **Or something similar