So you are running firmware 01.05.00.00 or later, using Bambu Studio 1.8.1 or later, and have done the following?
After the P1P Enclosure Kit has been successfully installed, please do the following settings on the P1P:
Click “Accessories” → “official enclosure kit” → “Upgraded”.
Does it give an error when about “Incorrect printer model” if you try to print? If not, this is probably how it is supposed to be, as this technically still just an upgraded P1P, not a P1S… although probably splitting hairs at this point…