Don't have a direct answer, but have you tried making the same short playlist on each, exporting as json from each, and comparing the files?
JSON isn't a specific filetype that is interchangable between multiple systems. It's just a way of organizing data as text. You can open it up in a text editor.
The format that invidious is exporting is for invidious. Invidious won't have the data in that json file organized in the way that piped expects, which is why it says it's not valid.
You might be able to reorganize the JSON or rename the property names to match the pattern that piped expects. You'd probably be looking at scripting something yourself though.