Do you think any/all individual medical information should be completely private?

First, we don't have funny names for our laws. That is an advantage, because that way we don't have the need to explain such funny names, or their meanings. And then we can't forget to explain them when it is neccessary.

Regarding your more specific question:

I believe that nearly all individual medical information should be completely private.

One exception is when the person owes such disclosure. For example you are a worker and you get sick so you can't do your job, then you have a duty to tell the boss/company that it is because of being sick (in such cases the boss does not need to know any further medical details), and you also have a duty to tell when that condition is over and you are able to fo your job again.

Another exception is when a person has special needs because of a medical condition and somebody else must provide for these needs. You cannot assert a claim without a basis. In such cases you need to disclose more specific details. For example a pregnant woman can claim maternity leave from work, then she needs to disclose the fact that she's pregnant. Or an office worker has spine problems and the company must provide a special desk and chair, then the worker must disclose some details of his condition to back this claim.

Should public servants need to publicly disclose health issue?

Not at all. I cannot imagine a situation where this is needed.

But there are some "very public" people like politicians or the pope, who usually disclose too many such details because they themselves think they owe this to the public.