Even I was getting the same Error with Azure Data Studio. That is coming up because you need Docker to run along with the Azure Data Studio. Per your post, i am not sure if you have installed docker or is your docker running in the background while you try to connect to the server(if docker is already installed).
In order to connect to a server, you need to go to preferences of your Docker settings and increase the Memory allocation from the default of 2GB to minimum 4GB (as SQL server needs min 3.25GB space). Save and restart the docker.
Once restarted, all you need to do is pull the docker image of the sql server and download it. this can be done by below commands on your terminal . FYI, I am using bash commands below:
Command 1:
sudo docker pull mcr.microsoft.com/mssql/server:2017-latest
This will pull the latest vesion docker image and download. Once done, you need to set your SQL authentication on the server for your database. Follow below commands:
Command 2:
sudo docker run -e 'ACCEPT_EULA=Y' -e 'SA_PASSWORD=<SetYourPasswordHere>' \
-p 1433:1433 --name sql1 \
-d mcr.microsoft.com/mssql/server:2017-latest
This sets your password and uses the port 1433 for SQL server (which is the default port). To confirm if the image has been created and the SQL server is running on docker, execute the below command to check log(s).
Command 3:
docker ps
To check all instances in your history of dockers( i.e. if you already had dockers installed before you are attempting this SQL connection/execution), run the below command and it will give you all the logs of all instances you have created
Command 4:
docker ps -a
or
docker ps -all
Once, you have completed above steps and see that the docker has created SQL instance, you need to go to Azure Data Studio and set the below credentials to access the server that you just created above using Docker.
Server: localhost
Authentication Type: SQL Authentication
Username: sa
Password: <Check Command 2 to see what you entered in the password where it says SetYourPasswordHere>
Hope this helps in your tryst with running SQL server on your MAC. All the Best!