Unfortunately, I don't own the P16s, but my experience is that Lenovo often installs screens that are not specifically designed for pens, which is probably why it doesn't work.

Since nothing is listed on the official site that pens are compatible accessories, I think that there is no pen support here either.

https://www.lenovo.com/ch...

What exactly do you need the pen for? Maybe I can recommend something as a workaround.