Do you have to meet Peach in the World Order?

After beating the game, Peach goes on to visit the kingdoms in her own terms.

I met her in the hat kingdom, but couldn't find her on the moon or metro city.

So I'm wondering, do you have to meet her kingdom to kingdom (kinda following in her steps) in the order on the map, or did I just miss her in those 2 (she can be met in any kingdom at any time, regardless if you found her in others)?

There certainly doesn't seem to be any order, at least not in my experience. I've met Peach on several of the worlds in no particular order. Each time, she mentioned visiting the Cap Kingdom. When I finally went there, she mentioned going to the Cascade Kingdom. I suspect the game intends to allow you to follow her this way, but there's been no rhyme or reason to how I found her.

In no particular order, and after each visit having her mention Cap Kingdom, I have found her in:

• Luncheon Kingdom
• Seaside Kingdom
• Lake Kingdom
• Ruined Kingdom

This article makes no mention of any requirements for finding her, and it looks like in Metro and Moon she is fairly hidden compared to the other locations. It seems to indicate that the only Kingdom that is gated is the Mushroom Kingdom - you'll need to find her everywhere else before she returns.