Cloud SQL Proxy (used by Cloud Run) does actually support Microsoft SQL Server. However, Cloud Run exposes this proxy only using "unix domain sockets" (and not local TCP IP addresses). Problem is, many mssql client libraries won't be supporting Unix sockets as the connection option.
If you can find a SQL Server client that has support for Unix sockets as the transport (see this), you should be able to use unix:///cloudsql/...
socket on Cloud Run to connect to SQL Server.
However, note that this is about to get a ton easier as Cloud Run is adding support for VPC Connector which will allow you to connect to Cloud SQL instances within the same network directly over their private IP address, and you won't need to use the Cloud Run’s feature exposing the Unix socket.