First of all, be honest with your teammates and boss. It's okay to tell you've burned out.

I'm sure they can relate and help you going through this and covering you while you're trying to recover from this.

This will also help them understand that they should avoid disturbing you during your healing vacation and make sure you will be on work-free mindset.

Take as much time as needed. Even unpaid leave if needed.

Wishing the best