Thanks to this article for getting me somewhere with the error message.
The issue is the necessary network protocols are disabled by default in SQL Server Express. I had to go to Sql Server Configuration Manager locally and turn on “Named Pipes” and “TCP/IP”.
After that, you need to restart the SQL Server Browser and SQL Server(instance) services.
While I did not have to, you may also need to check in “SQL Server Network Configuration” under “Protocols” for settings that need adjusted there.