Hi Jani Hämäläinen ,
Welcome to Microsoft Q&A platform and thankyou for posting your query here.
Could you please make sure that the SQL scripts are published before you are trying to use multiline code selection and editing?
I tried at my end and 'Alt+Shift+Up/Down' is working for both SSMS and SQL Scripts(when it is published).
Hope it helps. Kindly let us know how it goes. Thankyou