I purchased The game and most of the expansions on Steam. Then I recently found out there is a mobile app for iOS. I looked at and followed the directions on https://forums.obsidian.net/topic/92893-how-to-merging-desktop-and-mobile-accounts/. After entering in the PFID and the Secret Key, the iOS app is locked on the screen saying Processing... definitely waited for 5+ minutes several times and I made sure to get a new Secret Key each time.

 

My PFID is 419D4B760BF4248D

You need to have a Game Center account first. The merge process is hanging because it’s looking for an iOS account to integrate and coming back with nothing. Once you have two accounts (iOS and Steam) then it will go pretty quickly

That was absolutely the issue. I had Gamecenter disabled on my phone and it wasn't to get past that step. Turning on Gamecenter and then setting up my phone correctly allowed me to successfully join my iOS device to my Steam account copy.

Glad to hear you got that sorted out