TLDR: here is the URL to download the English (en-US) MSI installer for SQL Server 2022 LocalDb: https://download.microsoft.com/download/3/8/d/38de7036-2433-4207-8eae-06e247e17b25/SqlLocalDB.msi
For (my) future reference: here’s how I found it
- Download the SQL Server 2022 Express Installer
SQL2022-SSEI-Expr.exe
from the the SQL Server downloads page. - Open it in ILSpy.
- Save the Microsoft.Sql.Installer.UI.Externals.InstallerEngine.dll embedded resource to a new file.
- Open this file in ILSpy also and locate the
Manifest_Media_Express_en-US.xml
embedded resource, in which you will find a reference toSqlLocalDB.msi
, which combined with theDownloadRoot
URL just above it gives you the required location.

If you want the installer for other languages (e.g. German (de-DE), Spanish (es-ES)) then look in the Manifest_Media_Express
XML file for that language.