When I try to install PSO2 from the Microsoft store it gives me a list of hard drives to choose from; however the only one I have that is big enough to hold the game doesn't appear in the list. The only thing that really stands out to me for why it isn't showing up is that my other hard drives are formatted as NTFS and are internal drives while the other is an external drive and Exfat formatting.

I know the drive can run PSO2 as I've been playing the Japanese version on it with no issues and changing the JP installation to NA using the edition.txt will cause the game to load the English patcher and launch, although it still looks for the Sega ID rather than my Xbox Live account.

Looking at other apps on the Microsoft store it does seem like most (that I've tried) will recognize the external hard drive but there's a small number I've come across that don't, so it isn't a universal problem with the Microsoft Store.