Yes you can use Azure Portal. Just navigate to your Azure SQL Database resource, then go to the actual database instance running in that resources. On the options on the left is the Query Editor where you can view the database structure, run queries, etc.
To be honest though this is going to be an awful approach. I guess if you needed to make 1 quick change you could do it this way but if you intend to manage the DB, run queries, etc then it will quickly become painful. You mentioned you didn't want to install Azure Data Studio but that is probably the easiest and best approach. You can then write, save and run queries and do all the standard DB management stuff from your machine instead of using the browser. I cannot think of a reason why you wouldn't go this route.
If you really, really didn't want to use either then the only other option that comes to mind is using the Azure CLI but I cannot imagine how painful that would be and you'd need to know all the CLI commands to run to interact with the DB. It seems like ADS would be a more efficient approach. Even in Windows these are your choices so the fact you're running a Mac doesn't really change anything here.