I ended up fixing this without identifying the root cause. Once I tried connecting to the VM over SSH and accessing the database locally, I experienced the following errors:
Sqlcmd: Error: Microsoft ODBC Driver 17 for SQL Server : TCP Provider: Error code 0x2746. Sqlcmd: Error: Microsoft ODBC Driver 17 for SQL Server : Client unable to establish connection.
Following up on those led me to this GitHub issue, which provided a fix to my problem. It looks to have been a versioning issue - in my install script, I replaced
sudo apt-get -y install mssql-server
sudo apt-get -y install mssql-server=14.0.3192.2-2
and the problem went away.