For beginner-to-intermediate raster use cases where you want to direct the GPU yourself, WebGPU will cover most of what you're looking for with reasonably low cognitive overhead. It's at a roughly DX11/Metal level of abstraction, but with some crucial modernizations that reduce friction between WebGPU and the underlying APIs (pipeline layouts being the biggest one).

The main things it's missing for more advanced raster use cases aren't really GPU features as such, but low-level control over the driver. Unlike Vulkan/DX12, it does not permit (or require) you to manage allocations of individual resources in GPU memory, or perform your own CPU/GPU and GPU/GPU synchronization. The rationale (as I recall from some of the people working on the standard talking on GitHub issues or somewhere similar) was that the computational overhead of verifying that you've done these things correctly erases the gains from giving the user this level of control. For the web platform, verification that you're not going to corrupt memory or expose undefined driver behavior is non-negotiable. This explanation makes sense to me, and I haven't really heard anyone put forward a generalizable scheme that allows you Vulkan levels of control with efficient verification.