I would like to know how much he can write about my mental health, also considering that the academic work didn't suffer at all from this.
According to some of organizations: "The Americans with Disabilities Act recognizes that employers may sometimes have to disclose medical information about applicants or employees. " But also they claim: "The basic legal principle that employers should follow is not to reveal medical information about you unless there is a legitimate business reason to do so. But because that standard is fairly vague, there are laws which more specifically protect the privacy of your medical records, such as the Americans with Disabilities Act, the law which makes it illegal to discriminate on the basis of an employee's disability."
For UK you may find more information on NHS website and Equality Act 2010 Guidance for employees.
If you ask me I would say that it is not actually ethical to write about your mental health if your job didn't suffer from that. For some careers there are some health restrictions (e.g. pilots, surgeons, etc.) but I've never seen that for academic work. More to say, I know people who have GAD, OCD, etc. and they have never had significant issues in academic life. But I also have to say that people usually don't take year off because of mental health issue, especially not for GAD. From your post I can't see if the GAD is a main reason of one year off. If it isn't the main reason then I don't understand why your supervisor has a need to write it in recommendation letter. But, if GAD is your main reason why you needed to stay away from University than I don't understand how your mental health didn't affect your productivity when it is even though you continued to work. Whatever the case is, I wouldn't like that my supervisor writes "a mental issue" because for me it sounds serious and Generalized Anxiety Disorder actually doesn't sound due to prevalence "GAD affects 6.8 million adults, or 3.1% of the U.S. population"
Shortly, I don't think he should write about your mental health when you obviously continued to work. It is your private information, there are some laws about it and I am worried that you will be discriminate because of that.
My advice: Talk with your supervisor, find out why he thinks that he is forced to write it in recommendation letter (that is really strange) and please look more into the laws and send them to him if it is needed.