Basic and Stakeholder are access levels - not groups.
If you are implementing them through Group Rules, then this should be applied automatically the first time a user signs in to Azure DevOps. You might want to review your existing Group Rules.
I haven't experienced the behavior you are describing. Considering that this is a one-time assignment, it might make sense to simply go through this manually (depending on the size of your environment).
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hth
Marcin