Looks like you're in Adobe's FullScreen mode - rather than Apple's
Standard key is F to toggle modes, next would be full black background, then the 3rd would be back to regular 'windowed'.
The 'tool' itself should be the bottom of the sidebar, highlighted below in red...
pic from Photoshop, not Illustrator
If you can't make the window span more than one monitor, that may be the way you have Spaces set up.
System Prefs > Mission Control > 'Displays have separate Spaces' must be off for spanning to work.