When I try to add a private group via Mixed Resources > Add Resources in a plan, it does not show any results ('No results found'). Can you please help here?
Private Groups can be added to plans only if you are part of these groups. Due to their restricted visibility, you need to be a group member in order to add/use the group in this Plan, regardless of whether you have a (Technical) Admin role.
Check if you are a member of the private group and join if you haven't yet.