Should I disclose my mental health issues to a prospective (and former) employer?

Seconding Valke. If they ask why you quit, "health issues that are now being treated" is a sufficient reason. If they don't ask, don't offer the info.

If it were me, I would consider volunteering that I am excited to be interviewing for the role again, because I left the role only because I was having health issues that were starting to interfere with the level of performance that I expect of myself, and I wanted to ensure that [dept / team] were not affected. Fortunately, the health issues are now resolved, and I am eager to get back to [name specific goals / tasks / projects] that I enjoyed contributing / working on / developing so much, and taking them to the next level...blah, blah. Whether I would volunteer would depend on how much info I could gather about the impression my leaving / work issues left behind.

You sound like a perfectly normal employee. You went to work, did your work and met your deadlines. No one concentrates 100% at work, you need to slack off a bit if only to refresh yourself. So right there I think you have an over inflated understanding of what slacking off is. Don't mention it. As for quitting and the gap. Practice a one sentence explanation and then let it go. If you're being interviewed, you are qualified for the job and may well get it. "I left the position due to some health issues, which are now resolved. I really enjoyed working here and I'd love to pick up where I left off." Let them follow that up if they like, but they probably won't. Don't be surprised if it's not even addressed, or touched upon. If so, don't bring it up.

From the perspective of your previous employer, it's not clear to me you ever had a problem. There's nothing here to "explain". You did your job. You did your job well. You voluntarily quit to "pursue other opportunities". Quitting a job is not strange, provided you don't strongly criticize your former employers, which is often perceived as indicating you are a difficult employee. I don't know why you would bring up anything about your anxiety to a prospective employer, because your termination was not abnormal. From everything I read, it would seem as if your previous employer would provide a positive reference. In other words, what do you feel you have to explain? I think you're overthinking this. Most employers tend not to care too much how you do your work, so long as you do your work. You did so. Why are you worrying about it?

"Health issues, that are now well managed and will not impact my work" If you had IBS or an STI or a difficult miscarriage, or any other medical issues that is uncomfortable to discuss. You wouldn't ever need to tell your employer. You certainly don't need to tell an interviewer.

Basically if you have two people up for a job, completely identical, except one says "well, I have depression and anxiety," that indicates that they are both a higher-than-usual risk with regard to work performance and they're in a sticky situation because you disclosed this (i.e. they may not be able to legally fire you if the work performance drop is related to a disclosed health condition.) So they're certainly not going to hire the person that they might not be able to get rid of easily.

If you quit rather than got fired, and you met your deadlines, etc., is there any way to informally talk to anyone over there about what they think about you? If you left on good terms and had a good reputation, seems like chances of getting rehired would be good, and I wouldn't bring it up. I generally think gaps in employment are more troubling to employees than they are to employers. As a hiring manager myself, it does come up as a question, but in this day and time to be unemployed for a while is not unusual. If you do find out that they were glad you quit, or you know you have negative reviews from last time, what have you got to lose by acknowledging the problems and telling them what you did about it?

I would not, maybe you were travelling and bettering yourself in some way? They probably do not remember.

This behaviour became worse as my anxiety (mostly about work) increased and definitely wouldn't have gone unnoticed. You know your situation better than we possibly could, but you shouldn't assume the above to be true, no matter how much it seems to be the case in your opinion. I have often had the experience of going into a performance review feeling that I'd had a terrible year, it was a major drop off from last year, and I'd be given an official reprimand/improvement plan. Instead: "Exceeds Expectations" and a raise. With that said: Don't feel the need to bring it up if they don't, and if they do, "Health issues now being treated.