Other than running T-SQL queries in SSMS studio or Azure Data studio, SQLCMD utility can be used. We can go to Run > CMD and open Command prompt and run the queries from there using SQLCMD.
Using SQLCMD, you can run a single query or bunch of queries stored in a text file. Please see the use cases and the examples of SQLCMD here: https://learn.microsoft.com/en-us/sql/ssms/scripting/sqlcmd-use-the-utility?view=sql-server-ver15
The same option is enabled in Azure Data Studio that you have shared in the screenshot. This blog talks about the same - https://cloudblogs.microsoft.com/sqlserver/2019/09/10/the-september-release-of-azure-data-studio-is-now-available/
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