Is it good to mention about past health issues (explicitly, depression) and struggle with it in applications, personnel statements while applying for jobs? How much negative effect does it have?
More importantly, how much positive effect does it have? The application and resume is to get an interview. The interview is to get a job offer. Once you have a job offer, if you need accomodations, you should bring that up. At that point, they are interested enough in you to be more willing to negotiate.
If the health issues are an advantage in doing the job (not usual), then bringing them up might help. If they are not material to the job, and it's one you can do, then they are not important to mention. It's like mentioning your favorite color, or where you'd like to go on vacation: what does it have to do with the job you are applying for? Only mention what is pertinent.
The negative effect is that there will be an easy reason to pass over your application for someone else. Unless they have few applications to choose from, that will always be a negative. You don't want to give a reason to not hire; you want to give reasons to hire.
If you are being treated and taking medication for it when necessary, I don't think you should have to mention it, as long as you are competent and able to perform your duties when under treatment.
In the US, there are laws that prevent a potential employer from asking about existing and prior medical conditions.