DirectX is a Windows thing, so you'll just have those calls translated to Vulkan under the hood (DXVK). You'll probably get better performance from just setting it to Vulkan directly.
Edit: As some others say, for BG3 specifically, DXVK does a really good job. My personal experience is that "the best" option is very patch dependent. At launch Vulkan was best, then after a few patches did DXVK ran better, but personally I'm back to straight Vulkan, for no other reason than wanting to be a +1 in the statistics.
OpenGL is a bit like Vulkan, but discontinued since... 2014, with a single update since then. It was actually stopped because Vulkan seemed better, and both API's were maintained by the same organisation.
In general it's more likely to work on older devices, but would be less performant than Vulkan.
If you have an Nvidia GPU definitely pick DirectX. On AMD it's more of a tossup, depends on the game and the features in question but generally it won't need to translate OpenGL, so it has higher maximum performance potential.
To expand - DirectX is a proprietary Windows solution. Any time you pick it on Linux, it will run through a translation layer
OpenGL/Vulkan are cross-platform
OpenGL is to DirectX 11 as Vulkan is to DirectX 12
Microsoft kept the same branding, but also followed in Vulkans/Metals footsteps of using lower level calls to the hardware.
This makes the graphics drivers simpler, and can be way more performant because the CPU doesn’t have to do as much