Apple - Do programs keep running on macos when user switches account?

Yes, the applications will continue to run in the background. This happens with Fast User Switching and when Locking then logging in.

Monitoring

You can see the other users' applications are running through the Activity Monitor application:

• Applications > Utilities > Activity Monitor.app

To see other users' applications, select the menu item:

• Activity Monitor.app > View (menu) > Other User Processes

While they will all continue to run, they may not keep doing the same thing.  For example, if iTunes is playing a song, it will pause when you switch users.  I haven't tried it with the new "Music" app.

All apps can be programmed to know if they have a visible window so they can take actions and do more work in the background or less work in the background.

In the end, as a multitasking and multi user OS many processes can stay running when you switch the user for the built in screen.