checking state of a specific keyboard key in c++

Yes, CGEventSourceKeyState. You need to use the virtual key codes, not character codes. The Carbon header file Events.h contains enumerated constants for these codes.

Thanks! I suspect macOS is blocking it, though.

In trying to find how to implement that in a non-typical Mac app (I write plugins for Adobe Illustrator using their c++ SDK and Hot Door's CORE), I found that macOS often blocks keyboard activity. In Ventura's System Settings > Privacy & Security > Input Monitoring I added Adobe Illustrator 2023 to the list of applications allowed to monitor the keyboard. I've been using a CORE function to monitor key presses, which has worked well until recently, and still works well for others with an older OS -- I suspect CORE already implemented CGEventSourceKeyState so my workaround is not likely to work.

Where else in macOS Ventura could those keystrokes be blocked?

It's conceivable that System Settings > Privacy & Security > Accessibility could be needed. Try calling CGRequestListenEventAccess, which may result in a prompt to add some permission in System Settings.