Print Screen works, just have the window focused, at least in windowed full screen mode (fake full screen I think is named in this game options) because that mode works best with my FreeSync and frequent alt+tab on Windows 10. Then paste into an image editor. This just for a test.
For frequent use, I'm using GShade, which is "GShade is a highly modified ReShade fork & package with a selectively network-unlocked depth buffer and numerous improvements."
https://github.com/Mortalitas/GShadeget there, works fine with BG3 in Dx11 mode, haven't tested Vulkan, but GShade has Vulkan mode as well, just set that when installing.
You don't have to use any other function, just go into GShade settings and set a screnshot key (I'm using F11 for GShade settings and F12 for Screenshot, and specify where to place the screnshots, otherwise has defaults already set, use those if the the game doesn't already using those)
Regular ReShade should also work, I just already have GShade because some online games dosn't work with Regular ReShade and this is optimized for those cases.
I have the latest Fraps (overlay based image and video capture) and doesn't work with BG3, can capture only the BG3 launcher.
I'm just writing these for anyone looking after how to screenshot BG3 in future, since OP solved it already.
I'm using only 2 sharpen filters with very low adjustment values: AdaptiveSharpen.fx & Clarity.fx, and a very slight color adjustments Tonemap.fx because BG3 is very well done, and don't need more. Even has TAA antialiasing implemented and works great.
Of course no built-in screenshot function, that could be engine limitation maybe.
If you don't have any other way, GShade is great because you can uncheck everything and use just the screenshot function, the optional show FPS and clock, with very close to 0 performance impact.
Oh and 0 crash and 0 bugs so far -- single player mode only, after 20+ hours.