I do not see any Windows 11 drivers on the P2219H drivers page. Have you tried to install the Windows 10 driver in Windows 11 via compatibility mode? Have you posted the issue on the Intel NUC forum?
I have been using the P2219H monitor with no problems with laptop running Windows 10. I have a new NUC Phantom Canyon with Windows 11 and Nvidia GPU that is connected to my P2219H monitor. The NUC is set to not sleep and the P2219H to turn off the screen after 15 minutes. The P2219H does not always wake up after the 15 minute power down and indicates that there is no HDMI signal when trying to activate with a keyboard or mice movement. I have set PCI Express/Link State Power Management to off with no results.  Any suggestions welcome.
P2219H, NUC, Windows 11, not waking up