As someone who has done this since DX7, what you’re looking for is WebGPU either Dawn (Google) or wgpu-native (Firefox). WebGPU works. It’s 99% there across platforms for use.
There’s another wrapper abstraction we all love and use called BGFX that is nice to work with. Slightly higher level than Vulkan or Metal but lower than OpenGL. Works on everything, consoles, fridges, phones, cars, desktops, digital signage.
My own engines have jumped back and forth between WebGPU and BGFX for the last few years.