With the developer unable or unwilling to troubleshoot this and with insufficient in-built diagnostics, and with the use of FTP—FTP transmits login credentials openly and insecurely, and FTP is inherently incompatible with any modern network security that doesn’t also sniff traffic—and with (local?) logs somehow getting shipped around by email, I’d be considering a replacement app.
Ask them specifically how they send the message. i’d expect they’ll send via an ESMTP connection to a mail server. There are various PHP and Python and other scripts for this, and a direct ESMTP via TLS in Swift ot ObjC or such isn’t that difficult. Sending directly into iCloud under your iCloud login credentials, in this case. Maybe they’re using AppleScript to script the mail? But either way, that’s a lot of (potentially fragile) work for shipping around a local log file, rather than generating it and offering a Save As function. Particularly if the app is running in your local login session, but even a running-in-the-background app can be coded to and then asked to provide a file somewhere useful.
Ask for the path to the local logs, or if there’s a way to enable local logs.
Somebody is going to need to take a look at the app source code. Above is based on a whole lot of guesses.