Since itch does not support achievements, there's no way to check if the game was already finished in a previous save. So you can still force the game to unlock NG+!
Steps to do so:
1. Put on your hacker hat IRL (Mandatory! Send me a a picture!)
2. Locate your save files folder:
- For linux is ~/.local/share/godot/app_userdata/Trapers Platformer/
- For windows is %USERPROFILE%/AppData/Roaming/godot/app_userdata/Trapers Platformer
3. Create a new file and name it savegame.unlockables.save (file extension is important too!)
4. Put the following contents in it:
{"new_game_plus":true}
5. Save the file and start a new game plus!