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.
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.
They also have a script patcher that makes it so you can use any font. A really useful feature if you replace fonts in programs or games, but the program doesn’t fall back to a safe font if a character isn’t supported.