I don't know if I am an FPBer? Is that another net worth term? I don't know if I am, but I do own multiple homes and this is definitely an issue. I like to be efficient, and so in general I just double my favorite core wardrobe pieces, adjusting a bit for climate and style. I don't mind owning two (or more) of a thing if I wear it a ton. I may also buy a piece in slightly different colors - let's say it's a cashmere v-neck, I might buy in black for NYC and navy for Paris. This way, when I am putting outfits together I am really working with very similar elements no matter where I am.
For wildly differing climates, I think it's best to plan ahead and stock your closet - whatever size it may be - with the things you'd like best to wear if you were on a special vacation in that place. Keep your palette limited to start - colors you KNOW you will wear and that will work together - and think about core and complementary pieces. For instance, for a beach house, you may like sundresses as an everyday staple, so you will need sandals, and will also want cardigans/shawls/shrugs/pullover sweaters for going into air-conditioning. It can be helpful to go to designers you like that espouse a certain aesthetic for that particular climate and culture - so for instance when I bought my current beach house, which is EXTREMELY casual in a malibu-y kind of way - I did a big shop at James Perse, which fits that aesthetic well.
Otherwise YES you will feel you have nothing to wear, and will buy things that don't really work just to fill perceived gaps.
Once you have a basic closet, you can start to have more fun with accessories etc., but I think to avoid the last minute shopping, planning ahead and keeping it simple is key.
I don't use the styling apps because 1) it's a lot of work to set up properly and 2) I don't think I would open them
(i.e. if I need clothes, I can just go shopping--and don't need to stock my closet)