Shared memory, yes, with the goodies: atomics and barriers. We rely on that heavily in Vello, so we've pushed very hard on it. For example, WebGPU introduces the "workgroupUniformLoad" built-in, which lets you broadcast a value to all threads in the workgroup while not introducing potential unsafety.
Tensor cores: I can't say there are plans to add it, but it's certainly something I would like to see. You need subgroups in place first, and there's been quite a bit of discussion[1] on that as a likely extension post-1.0.
Yes, we expect to have a natural path towards explicit cooperative matrix multiply ops.
If you have a wishlist, we have an issue tracker! ;) https://github.com/gpuweb/gpuweb/issues
On NVIDIA GPUs, flops without tensor cores are ~1/10th flops with tensor cores, so this is a pretty big deal for inference and definitely for training.