You can create a custom keyboard shortcut in VS Code (And Azure Data Studio too) that gives you this functionality. Highlight code, press a button and execute that code in the active terminal, which just so happens to be SSH’d into a remote host.
Head over to Preferences->Keyboard Shortcuts (Picture 1) and in there you’ll find a shortcut called “Terminal: Run Selected Text In Active Terminal” (Picture 2). This is exactly what I want. Now, when I’m presenting…I can highlight the code…and what I highlighted gets copied into the terminal below and executed on whatever system is active in the terminal below. This could be either my local computer or a remote system over SSH.
Anthony’s use case is specifically around presentations but it could also be good for general use.