How to deal with unnecessary stress introduced by the supervisor?
It is not unreasonable for a supervisor to write emails in the middle of the night. I do it myself, and frequently at that (sometimes because I am honestly just working late, sometimes because I am in a different time zone). However, it is unreasonable to expect immediate response when you do so (more accurately, it is unreasonable to expect immediate response for basically any email, as the medium is fundamentally asynchronous and nobody should expect you to have your email open all the time).

That said, a significant part of the problem also appears to be your own mindset. You can't realistically change when your supervisor sends you work, but you can definitely change when you read it, and when and how you react to it. Just not reading emails in the night is a big start. Many people do it, and you do not need to have a bad conscience when you do it as well. A second part of this is also to not interpret every email as implicitly highest-priority. Try to assess what a realistic timeline for any given work task is - if your supervisor does not specify you don't need to assume it needs to be done next thing in the morning.

One problem that you may face is that you have by now trained your supervisor that you read and react to every email at any point in time. Even if it's unreasonable, it is somewhat understandable that this is by now how your supervisor thinks you work. The most pragmatic way is to change things gradually over time, combined with a non-accusory one-on-one talk with your supervisor that you are unable to deal with your current work mode. Don't use the words "you are stressing me out" or anything else that puts the token and blame on him. Say that you are stressed out and need to change how you work. The goal is not to elicit a different behavior from him (although this may also come out of the meeting as a sideeffect), but to communicate to him how you plan to address your stress-related issues going forward.