Applications cannot do that. You cannot prevent the user from switching to another app, and even if you could, you can't show that other app's menubar or make its windows appear to have focus when they don't. The closest you can come to preventing app switching is using old-style fullscreen capture plus disabling global hotkeys (you know, like how a lot of old games work), but when you're doing that, the user can't even see other apps, much less think they've got focus.

As far as I know, to do things like record keystrokes or interfere with the UI of other processes, an app on macOS has to be manually permitted through System Preferences -> Security & Privacy -> Privacy -> Accessibility.

Steam's in-game overlay feature and even some functions of the built-in Automator utility have to be allowed from there.