For me it was quite confusing to find the 2019 version of LocalDB and it is not a streamline process to upgrade your local default instance.

The easiest way to upgrade your LocalDB instance to 2019 is:

1. Download the LocalDB 2019 installer by using the SQL Server Express installer.
   https://go.microsoft.com/fwlink/?linkid=866658
   
   1. Run the installer and select “Download Media”.
   2. Select “LocalDB” + click Download.
2. Before running the SqlLocalDB.msi installer, delete your current MSSQLLocalDB instance:

sqllocaldb stop MSSQLLocalDB
sqllocaldb delete MSSQLLocalDB

4. Run the new SqlLocalDB.msi (2019) installer. It will create a new MSSQLLocalDB instance.
5. RESTART YOUR PC! (Otherwise MS SQL Management Studio will still tell you you have an old version running, etc. etc.)
6. Now you can re-attach your original databases one by one using SQL Server Management Studio (RClick + Attach…)
7. Done.