Hi, and welcome topthe Apple (user-to-user) Community!
Re: "MacBook Air accessibility Keyboard; minimizing the keyboard takes up the entire screen"
Seems you can easily "Resize" the Accessibility Keyboard:
While you’re using the Accessibility Keyboard on your Mac, do any of the following:
- Make the keyboard bigger or smaller: Drag a corner of the keyboard.
- To resize it without keeping the proportions, click the Panel Options button
in the top-right corner of the keyboard, then choose Resize Proportionally (to remove the tick). - Reset the keyboard to the default size: Click the Panel Options button
in the top-right corner of the keyboard, choose Zoom, then choose 100%.
More info: How to: Use the Accessibility Keyboard on Mac - Apple Support