logic pro

Hi Emmanuel3jo, the first troubleshooting step is always rebooting the Mac (not in Safe Mode, but a simple restart). Most macOS software glitches could be fixed just by doing that. Restart, then sign into App Store with the Apple ID used to purchase Logic Pro. Also, take note that the current Logic Pro version is 10.7.4. I suppose, if you just purchased the app, that's the version you have.

I’ll assume the same Apple ID is in use everywhere. If not, start there.

If there is an add-on VPN client app involved somewhere, remove it, and restart.

Boot into Safe Mode, and try the update again.

Start up your Mac in safe mode - Apple Support

Logic Pro is updated using the Mac App Store.

Use the App Store to update apps on Mac - Apple Support