for all intent and purposes, azure sql edge is sqlserver 2019. use its docs.
you should download azure data studio for the Mac:
if you correctly exported the port 1433 you should be able to connect
server: localhost
authentication type: SQL Login
user name: sa
password: <your sa password>
to work with dotnet you have several options
nuget Microsoft.Data.SqlClient (AdoNet) is the preferred for SqlServer (replacing System.Data.SqlClient)
you can also use entity framework: Microsoft.EntityFrameworkCore