Ergo, when treating the Federation within the context of the fictional universe it inhabits, we have to treat it as a state.
But if enough contradictions to that exist, then it shouldn't be too difficult to accept that the UFP could be something other than a state, and
something other than a federally or confederally tight or loose cooperative of states. A descriptive approach to analyzing this futuristic construct might be better than one that tries to fit it in assorted historical molds.
As for "Vulcan exhile" -- what makes you think that the Vulcan government even knew that Kirk and Co. were at Mount Seleya? It's entirely possible that the Vulcan government no more knew they were hiding out there than the State of Montana knew that the Unabomber was hiding out in their state.
To operate a starship from a starport, no matter how much a "dirt strip", would seem to be an operation any government would like to be aware of if it happens on their dirt... And one would assume Vulcan keeps at least some sort of public eye on its celebrities such as high priestesses. But it could always be argued that this eye was deliberately turned away, and that Vulcans simply kept saying "No, absolutely no Earth fugitives here - would we lie to you?"...