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I have a 2019 MacBook Air, and a 2021 iMac. I am able to use one mouse and keyboard to control both screens.
I am trying to move a word document from my MacBook screen to my iMac by pressing and dragging but it stops at the edge of the screen and doesn't move to the iMac screen.
MacBook Air 13″, macOS 14.7
I presume you mean Universal Control:
Universal Control: Use a single keyboard and mouse between Mac and iPad - Apple Support
If so, that doesn't connect the two screens together so they can operate as one. Universal Control allows you to use the keyboard and mouse on each device without having to reconnect the peripherals. It also provides a "universal clipboard" so you can copy and paste between the devices and can drag-and-drop files in some cases. But unless I've completely missed something, you can't drag an app's actual window from one screen to the other, if that is indeed what you're trying to do.
Regards.
You should be able to drag the document file between one Mac and the other.
If you are trying to drag the Word window, that as mentioned is not going to work.
Find the file in Finder, and drag it to the edge of the screen and keep pushing the mouse until it moves to the other Mac. Then let it go.
Make sure you drop it either on the desktop or Finder.
click here ➜ Universal Control: Use a single keyboard and mouse between Mac and iPad - Apple Support
Airdrop may be easier to get to work though.
Those Macs are new enough that you could set either up as an AirPlay Receiver, and use it as an AirPlay screen for the other Mac. Note that AirPlay is a lower-quality connection method than a hardware connection to a real display, so the quality might not be good enough for what you are trying to do.
Still, since you already have the Macs, it wouldn't cost anything to play with it.
Continuity features and requirements for Apple devices - Apple Support
Moving between screens
