How do I avoid photobooth when attaching photos to messages/emails?

Photo Booth is installed as a part of the system. You can only uninstall it by modifying the system - you would need to disable the System Integrity Protection. It would not be worth it, as it is not Photo Booth that is causing the problem. The Media Browser is showing you all items, that are compatible with the application that is using the Media Browser to access photos. As the Photo Booth library is usually smaller than the Photos Library, it will be faster to be ready and appear. But it does not stop the Photos Library from appearing. Photos is just incredibly slow now to appear at all, probably because the Photos.app is no longer creating and saving Previews of the photos for the Media Browser, to save storage. So the previews need to be created over and over again.

To access my Photos Library from Apple Mail I find it quicker to use Mail's own Photo Browser instead of using "Attach". Have you tried it? After clicking the Photo Browser icon in the Toolbar in Photo, I can instantly select the Photos Library.

Sometimes it takes just a long time for the Photos Library to become available under "Media > Photos".

How long are you waiting after going to "Media > Photos"? Occasionally it took several minutes before the Photos Library finally appeared. It seems to help to keep Photos open and running, while trying to use photos in other applications. Are you using Apple Mail or a third party app?

You can only use Photos from the Media Browser, if the application is compatible with Photos. It should work with Apple's own applications, like Mail, Pages, Keynote however. Other applications may need to be upgraded to a more compatible version.