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It appears it is one Mew per Pokeball Plus, I received the Mew on Lets Go Pikachu, then started a game on Lets Go Eevee, delivered Oak's parcel to unlock the functionality to communicate with the Pokeball Plus, however was told "This Pokeball Plus doesn't contain any Pokemon presents." I then went back to Lets Go Pikachu on and put Mew on the Pokeball Plus to go for a walk, then tried again to receive him on Lets Go Eevee, however was told the Pokeball Plus doesn't contain any presents. You also can't return a Pokemon from a walk on a different game, otherwise you get told someone else Pokemon is on the ball and the results from the walk will be deleted. Screenshots below of when i received my Mew: This appears when the Pokeball Plus is connected for the first time: The receiving Mew process: Message that is displayed when trying to obtain a Mew on a different game, after already receiving a Mew: Message displayed when trying to take a Pokemon from a different game for a stroll with a Pokemon already on the Pokeball Plus from a different game: If nothing else screenshots to preserve as much as this unique event as possible. It's going to be a rare thing getting an event Pokemon on a unique piece of hardware like this.

I can confirm that all mystery gifts are done the same as Mew and Chansey. They are not stored on the save.

I wonder how many greedy scalpers are going to grab up a ton of Pokeball Plus, then sell them for twice/x-times the price once they are no longer offered for sale with Mews inside. I have no idea how this hardware works. But the point I wanted to get at, is that I wonder if there's a way to wirelessly communicate(similar to wc7full RAM dumps) and extract the data from an unused PBP, and re-inject the data at any given point. Therefore preserving the original event the way it was intended.

@InsaneNutter I took screenshots too, but I've been too busy playing, and not sure if they're as detailed as yours. I've added them to the event gallery

Gender is locked on the wonder card, even if the gender ratio is random. This is the process for gen 6: Meaning wc6full is random -> when sent to 3ds -> becomes wc6, stuck at male or female before user even redeems it.