The URL for updating the indexes does not look correct to me. First off, is your Organization ID really a GUID? Ours is just "1".
Next, you are not referencing a file cabinet, so I am not sure how that URL works. What I have used in the past would look more like:
https://my-site-test.docuware.cloud/DocuWare/FileCabinets/{file cabinet GUID}/Documents/{DocID}/Fields
You do not need the Account, Login, or Organization any longer because you are already authenticated. (Also, you have slashes doubled up between the site URL and "DocuWare".)
We then use XML post data for the indexes, a collection of Field nodes inside an enclosing DocumentIndexFields node. We use a POST.
My guess is that you are getting a successful result because that is the success of logging in. It is not actually trying to set the indexes because you have not told it which file cabinet you are operating on, and maybe because you are using a PUT and not a POST?
Good luck!