It is possible to install and run SQL Server Express 2019 and 2022 on the Apple M1 chip, but it is not officially supported. Fortunately, the root cause of the issue is not in the SQL Server itself, but in the installation. I've created a script which will install SQL Server Express on Windows 11 in a Parallels VM on Apple M1. You can find it here MSSQLEXPRESS-M1-Install.