Multirepository not supported when uid is in payload

1. install 9.10
2. setup multi-repository environment

Following this documentation:
https://doc.nuxeo.com/nxdoc/document-resources-endpoints/#updating-a-document

One can update a document through REST.

Using this url:
http://localhost:8080/nuxeo/api/v1/repo/[repositoryId]/id/[documentId]

With the following payload:

{"entity-type":"document","uid" : "{documentId}", "properties":{"prefix:propertyName":["value"]}}

Fails to update the document with a 404 error.

It seems the issue is the session is opened in the default repository in this case:
https://github.com/nuxeo/nuxeo/blob/9.10/nuxeo-core/nuxeo-core-io/src/main/java/org/nuxeo/ecm/core/io/marshallers/json/document/DocumentModelJsonReader.java#L132

Please note that removing the uid from the payload works fine.
------------------------------------------------------------------------------------------
In this case, the repositoryId passed in the URL is now also set as a request attribute when set in the WebContext by APIRoot#doGetRepository.
It can then be retrieved by SessionFactory#getRepositoryName and RenderingContextImpl#getSession.