Nice observation, elempi. Let me say a few things. From my point of view, I definitely agree with what you spotted there - Gandalf indeed has these several different "personalities" throughout the books, the most striking, which probably everyone notices since it is also an "outward change" is the Gandalf the Grey/Gandalf the White transition. The others are also true, the way you mention them.
But, at the same point - and I would especially emphasise it in regards to what you have said about the wizard ("This time, I am a conjurer of cheap tricks"
) at the Unexpected Party - I would say that these can also be seen as mere personality changes, or different sides of the same personality in different situations. Think about it. A person often acts differently when at home with family, in a circle of friends, or at work, when being a high-placed politician, or as a conscript in the military or in the middle of a war. It can all be the same person but you'd probably agree he might seem very different in those different situations.
And that's it, in my opinion. When Gandalf is in the Shire, he is "resting" from his daily duties - a bit, even though even here he has his own agenda and is trying to get Thorin to take Bilbo along for some reasons - but you can see it everywhere, even in LotR. Among Hobbits, who are generally isolated from the worries of the world, Gandalf is on "holiday" and he can make fireworks and just have fun. Indeed, I think "being on holiday" is the best term - it's probably the only holiday Gandalf had ever enjoyed in Middle-Earth. So therefore, he acts like that* Wizard.
*One small note. I object to the term "Nordic Wizard" you have used. I know you used it because you are aware that in other cultural context, Wizards can look differently - like e.g. some African shaman, to show some extreme case - but it is certainly not "Nordic", the thing you are talking about (if we both think the same thing). My country is not "Nordic" in any sense, yet the image of what "wizard" is is very much the same for me. "European", perhaps, in some way you could say, or whatever. I think "Wizard" suffices. That's just a note. You really made it sound - to me - as if that Gandalf should be something "alien" to me, which it is not. It is a Wizard, as much as I know Wizards from mythology I've been hearing from childhood. Unless by "Nordic" you mean "more northern than the Mediterranean". And even then who knows.