I have posted this question already in the Sonoma user forum but did not get not get an answer, so I try it here once again:
When I start the update from the system preferences then the update is downloaded what takes around 18 minutes. Then it seems that the installation is started with the messages "macOS Sonoma 14.4 vorbereiten" and "noch ungefähr 30 Minuten" and the progress bar somewhere in the middle. But after the time of more than 30 minutes the messages and the progress bar are still the same. The activity monitor shows the process com.apple.MobileSoftwareUpdate.UpdateBrainService that takes 20 to 30 percent of CPU and never stops. When I kill the process (recommended solution) the software update fails. I have found a log file MobileSoftwareUpdate/restore.log where the following sequence occurs 16 times:
CleanupPreparePath main() started setSystemTargetUUID will use / as the target Found update container: LPAPFSContainer: AppleAPFSMedia, UUID: A2FEC6B7-7C15-40B9-8B04-AE8CD30A9117 Found update volume: LPAPFSVolume: Update, Mount: /System/Volumes/Update Will open restore file at: /System/Volumes/Update/restore.log
A similar problem occured already in 2020 on Intel Macs. It seems that the problem is only on Intel Macs. I have no software installed that would influence the system and I have disabled all background processes in the system preferences.