Per (a limited) community consensus at [1], the ability to add users to, and remove them from, the GWToolset user group, should reside with Commons bureaucrats rather than with administrators.
The testing period for the GWToolset tool is now finished, and there is enough consensus to let bureaucrats handle its assignment from now on (as most users involved with the GWToolset project have already been added to that user group).
References
Version: wmf-deployment
Severity: enhancement
URL: https://commons.wikimedia.org/w/index.php?oldid=119975868#GW_Toolset_right