macOS ships no keyboard shortcut for it, at any version through macOS 27. Its own window shortcuts (macOS 15 and later) cover halves, fill and centre on the display the window is already on.
Three ways to get one: bind the Window menu's Move to command yourself, use Rectangle, or use Hammerdeck, which also swaps everything on two displays in one go and undoes either move with one key.
With a second display connected, most apps' Window menu has a Move to <display name> item. macOS lets you give any menu item a shortcut:
Move to DELL U3224KB.It costs nothing, and it has three limits: the title must match character for character, so a renamed or replaced monitor breaks it; you need one shortcut per display rather than one for “the next one”; and apps without a standard Window menu don't have the item at all.
Hammerdeck is a free, open-source menu bar app. Window Snap is on from the first launch:
One key throws a window to the other display and back. The second half is a rule rebuilding the layout on replug, covered in putting windows back when a monitor reconnects.
Every shortcut can be changed in Settings, and each press flashes the name of the action that ran, so a wrong key is obvious. It needs the Accessibility permission to move windows, and explains why before macOS asks.
If a display throw is all you need, any of them will do. Hammerdeck is built for the setup where you do it all day: the swap, the undo, and layouts that rebuild themselves. The side-by-side comparison lists what each one does.
Hammerdeck is free and open source (GPL), notarized by Apple, and runs on macOS 13 and later.
Download HammerdeckOr brew install --cask kouxing2000/tap/hammerdeck