Welcome to the Forum, @emcampbe! 
I don’t have Scale X, but I use Scale S, and my experience with using the Settings ➜ Export Data feature is that this causes the Wyze servers to send me an e-mail message with a spreadsheet/workbook attachment that contains my (poorly formatted) data. If that’s what you’re doing, then I’d expect Wyze to be sending you an e-mail message, though other users have reported difficulty receiving those in the past. I don’t know if a reason for that has ever been determined.
I say that just so you don’t expect the Export Data feature to fix the Apple Health sync issue, which I think is a separate problem. I don’t use Apple Health, so I don’t know if it allows you to upload/import data from another source (like a workbook) even if you receive that data.
I have never had this happen. In fact, I tried it again just a few minutes ago and received the e-mail message with the past year’s worth of data in a workbook within seconds. I wouldn’t expect this process to require any sort of human intervention, so I can’t account for any delays you’ve experienced. 