What file format is used for Minecraft worlds on the PS4? How can I tell if a downloaded Minecraft map is PS4 compatible?
The root cause of your problems is that the term "PS4 edition" is ambiguous. On one hand, there's the MineCraft edition that has been on PlayStation consoles since PS3, known as Legacy Console Edition. On the other hand however, there's Bedrock Edition which results from Pocket Edition, Windows 10 Edition, Gear VR Edition and Fire TV Edition being merged in the Better Together Update, and which has since been released on PS4 as well.
You have Legacy Console Edition, whereas the .mcworld format is used by Bedrock Edition. And as you noticed, the save formats are not compatible out of the box.
Fortunately, you can convert the worlds using Universal Minecraft Converter. I've been looking into whether MCEdit Unified can be used as an alternative, but that doesn't seem to be the case. As VanguardPlayer points out, you additionally need to assign the save data to your profile, which you can do with Save Wizard. Be warned that it's paid software, costing a whopping $60. Apparently, a software called Xploder is capable of assigning save data as well, but there's a few problems with that:
- I couldn't find a clean direct download,
- it's closely associated with cheating and dirty business (might be the cause for point 1),
- the price tag is supposedly the same anyway.