There is a WebAssembly proposal called "Threads".

https://github.com/webassembly/threads

"This proposal adds a new shared linear memory type and some new operations for atomic memory access. The responsibility of creating and joining threads is deferred to the embedder."

As for the current status, it is listed on the proposals page: https://github.com/WebAssembly/proposals

The "Threads" proposal is in "Phase 3 - Implementation Phase" which means it's starting to be implemented, but it hasn't reached "Phase 4 - Standardize the Feature" where 2+ browsers implement it. The final stage would be "Phase 5 - The Feature is Standardized. See https://github.com/WebAssembly/meetings/blob/main/process/ph...