Does JSON-API support workflow_id?

I can’t find any mention of workflow_id in the documentation. In the section on contract creation, there is a part that mentions a meta variable which can be used e.g. for setting the command_id , and I tried adding the worklfow_id in there to no effect.

I’ve also tried looking through the daml codebase, and can’t find any mention of workflow in the source code.

Is this not supported through the JSON API? Why not?

No; it was removed in Daml SDK v0.13.33, while JSON API was still experimental.

Broadly speaking, as a matter of design, points #5-7 here.