Nothing about either of these shots is subtle. In The Christmas Chronicles, the camera lingers on the security guard far longer than any movie has any right to linger on a nameless character we'll never meet again. This is Netflix taking your grubby little face in its perfect, digital hands and pressing it to the screen: Look. Look at this. Notice this. Do they think their viewers are so stupid they have to shove their own allusions into our eyes? Or is something bigger going on?
This is where things get tricky.
We can actually measure (we can't actually measure, but I'm going to do it anyway) how close these universes are to our own using their respective modes of self-referentiality. The Christmas Chronicles featuring a nameless side character watching Stranger Things, one Netflix's most popular series in reality, would suggest that the movie exists in the real world, or at least a world close enough to our own to work more or less the same as ours does -- and it means that an alternate-universe Netflix also exists in this universe. Presumably, that would mean that The Princess Switch and both Christmas Princes are also movies in this universe -- except for the fact that The Princess Switch contains its own version of Netflix as well.
Neither A Christmas Prince, nor A Christmas Prince: The Royal Wedding feature anything untoward other than a striking degree of self-referentiality to their own ridiculousness. When the father of our protagonist is recast in the sequel, he walks out of an airport feeling like "a brand-new person." There's even a moment that suggests the writers of the sequel had read -- and enjoyed -- nitpicky criticisms of the first movie and the badly designed brand logo of its fake magazine.
So, whose universe is whose? The Princess Switch's mood is too fantastical to be a representation of the real world, and it's also an amalgamation of a bunch of other movie tropes rolled into one. It's already aware enough that it's a movie, whereas the more grounded tone and the appearance of something other than Netflix holiday content in The Christmas Chronicles indicates its universe must be the prime universe. The Christmas Chronicles was also produced by big Hollywood folks, including Chris Columbus, the guy who directed the first two Harry Potters, Home Alone, and Mrs. Doubtfire. That means A Christmas Prince and A Christmas Prince 2 are movies in The Princess Switch's universe, which is itself a movie in The Christmas Chronicles' universe.
But then how do we take into account the characters of A Christmas Prince being able to watch the royal wedding -- the REAL royal wedding, the royal wedding of OUR world -- on their TV in a short teaser video posted a few weeks before the sequel dropped?