Try to run version 0.2.0 of @capacitor/live-updates, which is required if you want to use Capacitor v6, and it will break during build on iOS. The error is:
/@capacitor/live-updates/ios/Plugin/LiveUpdates.swift:109:1: extraneous '}' at top level
v0.2.1 has been released to address the issue, thank you for reporting it.