This is one of the features of Azure DevOps. Stakeholders by default won’t be able to create or edit or delete any tags on the workitems in Azure Boards. If a stakeholder has a necessity to update or create new tags then the user with stakeholder license should be upgraded to basic license.
Once the stakeholder has been upgraded to basic license, ask the user to logout/login in again to check whether the user is able to create/edit the tags. In addition to the tags limitations, stakeholders have also other limitations like not being able to delete workitems or move workitems out of the project eventhough the stakeholder might have admin permissions to both the projects. If your are adding a user with stakeholder permission as one of the Project Administrators, it would be better make sense to upgrade the user to Basic access as a user with basic access would be able to do a lot more as a project administrator like reordering backlogs, changing the priority and deleting the unwanted workitems etc.,