Can you use macOS "log stream" or "log show" to get messages from connected iOS devices?
log collect --device lets you retrieve log archives that can be passed into log show --archive system_logs.logarchive with all the options you're familiar with.
Use log collect --device to automatically guess the device you're referring to.log collect device-name="Maxs iPhone" or log collect device-udid=abcdefg to collect from a particular device.
log collect --output /your/path will save it to your specified file name or directory. If --output is not given, your output will be in the current directory as system_logs.logarchive.
Note: I occasionally get errors about log: failed to create archive: Device not configured (6) or log: failed to create archive: Connection reset by peer (54) but if I just rerun the command it'll sometimes work 🤷🏾♀️
i'm not sure this helps but if you have access to the source code of the app you want to log, you can add NSLog prints and send them to a file, which you can view/retrieve with iTunes Connect (there is a small change you need to add to the .plist file about file-sharing).