In SQL Server Management Studio (SSMS), you can create multiple cursors across multiple lines with alt + shift + up/down. Because of its VS Code foundation, Azure Data Studio has similar functionality built-in. Creating multiple cursors in Azure Data Studio can be done directly on adjacent lines, at user-determined locations, and at instances of a selected string.

tldr; ctrl + alt + up/down in Azure Data Studio

Multi-Line Cursors

Using ctrl + alt + up/down, you can add secondary cursors immediately above and below your primary cursor in an Azure Data Studio query editor.

User Selected Locations for Cursors

Holding down alt, you can click anywhere in the Azure Data Studio query editor window to place additional secondary cursors.

Current Selected Text Cursors

After selecting a segment of text, using ctrl + D cascades through the query editor creating secondary cursors wherever the text is found. (one location at a time)

Helpful Documentation

If you’re using Azure Data Studio frequently, it’s worth your time to become familiar with VS Code editing functionality: https://code.visualstudio.com/docs/editor/codebasics
There’s even a handy single-page PDF: https://code.visualstudio.com/docs/getstarted/keybindings#_keyboard-shortcuts-reference