According to website Gematsu, there is a new Painkiller game in development by Saber Interactive. It will be published by a division of Koch Media known as 'Prime Matter.' Here is a link to the article:
https://www.gematsu.com/2021/06/new-painkiller-game-in-development

This is the first I've heard of this. I wonder if it's been cancelled already.

The developers web site still shows it as TBA. just scrol down and you see it

primematter.gg/en-us

perennius