As per the docs here, https://flowable.com/open-source/docs/cmmn/ch08-REST/#create-or-update-variables-on-a-case-instance, I think the PUT url:
PUT casecase-instancesruntime/case-instances/{caseInstanceId}/variables
is wrong.
Good catch. Fixed here: https://github.com/flowable/flowable-engine/commit/98579d4c76e9340dd5006d05f4ab4c803b8f34d6