Symptom

SignificantOfflineInstaller Error: 0: 2021-02-09 14.31.35: InstallSqlLocalDb: Installation of Sql Local Db Express failed
SignificantOfflineInstaller Error: 0: System.Exception: MsiExec returned: 1603 Fatal error during installation
at Assert.Base.Install.InstallSupport.InstallSqlLocalDb (Task task)

Cause of error

We do not know why it went wrong, 1603 means "something is wrong somewhere".
Unfortunately, the installation program does not provide any additional information, but you must troubleshoot the installation of LocalDb separately.

Create a log file

Analysis

Were there any error dialogs while running the command?
Created an install.log? In that case, send the file to Signifikant for diagnosis.