To troubleshoot problems, we need to be very precise. Installing the application and saving backup files are separate and unrelated actions. Neither has anything to do with the other. In fact, the two actions you mention, installing on your Mac and saving the backup file, could happen on two different machines.
Did you install and/or update according to this Guide?
If so, when importing the business with the Add Business button, you can navigate to any accessible drive to find the backup file you made using the cloud edition. Select it, and you should be good to go.
Note, though, that all of this is entirely separate from any problem you may have with the file extension on your backup file. Can you tell me where exactly you created the backup file and what its full name was there? And what have you done with it since to get it to wherever you’re having trouble, and what is its full name there?