Support for DX12 and Vulkan were tentatively begun in early versions of ReShade but then dropped and put on hold, Crosire recently posted just a few days ago on why Vulkan wasn't supported by ReShade just because supporting these low-level API's would be a lot of work though perhaps in time ReShade could support them.
(EDIT: From what I can tell of some of the Github commits and data at least.)
Github and open sourcing helps too but there hasn't been that many commits for ReShade itself because it's a pretty complex piece of software.
For Wolfenstein unlocking the debug console and tinkering with the cvars help a bit, Vulkan however (And DX12) also limits shader editing and viewing (Vulkan uses a different shader format entirely, SPRIV or what it was called if i remember correctly though it supports GLSL too.) so using tools like 3D Migato or similar to straight up alter the existing games shaders isn't going to help either.
Not too sure how much drivers and such play a role either, Vulkan has a little launcher software too which is also updated with new bug fixes and features in addition to Vulkan API support in the drivers (Both AMD and Nvidia have made a lot of improvements here.) and then there's the games implementation of the API as well which I would assume depends on which SDK version of Vulkan it was built against. Might not matter too much overall for ReShade and how it would work for the API though hooking into and wrapping shader injection support.