Why would those be dramatically different anywhere? It's the same few choices of mini-splits from the same few Japanese/whatever conglomerates across the world, with known cooling abilites (measured in the same units, BTUs) and with known energy consumption (kwh) (and power in watts). The hotter the place you live in, the more power it's gonna draw, and the more BTUs you'll need. Also the bigger the room, the more BTU you'll need.

Fujitsu and Mitsubishi both have popular units that are basically the same the whole world over, with minor regional changes. There really isn't that much variation though. There are obvious differences, a mini-split in a hot part of the world is going to be working harder than a mini-split in a cooler part of the world. Humidity will differ as well.

It's a large home appliance. You need a pair of strong people to drive over to the customer's house, bring it in their house, locate the right place to install it, unbox it, support it, wire/pipe it up correctly, and then give it power. The Big Mac index gives the difference in price between Japan in the US to be $5.79 vs $3.11 in JP (in 2025), and meanwhile $1k vs $10 is, well, 10x.

There's something at work here, but it's not due to variations in the difficulty of unboxing a large metal thing, drilling holes, running some tubing and then powering it on.

The units themselves are not significantly more expensive nor any more difficult or time consuming to install.