A new Alan Wake 2 update has been deployed today on PS5, though you won't find any PS5 Pro-specific enhancements in its patch notes. Remedy has said it needs more time to research "a few things on the Pro when it comes to improved performance" as the update available at the PS5 Pro's launch made the Performance Mode worse than it is on the base console.
Addressing the PS5 Pro performance issues, Remedy said on Twitter: "The PlayStation 5 update (1.200.005) does not contain anything PlayStation 5 Pro specific, but we wanted to acknowledge that we are seeing your feedback. We are still researching a few things on the Pro when it comes to improved performance. We'll keep you posted. As PS5 Pro support was a work of many months, it will take the team longer than a few weeks for changes and improvements."
Alan Wake 2 has been one of a few upgraded PS5 titles that have experienced teething issues with the PS5 Pro, others being Silent Hill 2 and Star Wars Jedi: Survivor. The former is currently facing problems with shiny reflections and quite noticeable blotches on the screen (even after a patch tried to clear them up) while the latter has flaws relating to image quality.