The specific badges you are referring to were placed in the Kunena forum area by the CBSubs Plan Image integration plugin.

I am now using membership pro.

Looks like you were a member 4+ years ago (2016).
So you do not have the latest builds.

With your extensions, can you manage user groups in a similar way?

Perhaps there is a way to manually do this and Kyle might be able to help when he is back online.

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CBSubs can manage usergroups. It only handles 1 usergroup per plan. It will automatically remove the usergroup when the plans subscription expires. If you need deeper control over usergroups you'll need to combine CBSubs with CB Auto Actions for the time being. CB Auto Actions will allow you to add, remove, replace, and even create usergroups based off subscription.