I checked the error log on the server and the Braintree Gateway was not what crashed your site.
What crashed your site was there were files from both 4.10.0 and 4.9.82 versions of Event Espresso 4. I’m not sure how things got to that state, but after removing, then reinstalling files from one version only, 4.9.82, all is well. The Braintree Gateway plugin is now activated and no more errors are thrown.
I can advise to update to version 4.10.0.p when you have a few moments. You’ll do well to make a backup of your database first. After you click the update now link, you’ll be prompted to upgrade the database which will take a few minutes.