If you have to go to HR to get accommodations, you should get a different job. In my experience, when a manager won't make accomodations without that, they won't do it with it or they'll hold it against you. My manager at Intuit just said "no" to every single request my doctor had written down. HR's response was to just shrug their shoulders and say they have no authority. The next company just laid me off for having too many doctor's appointments.
The best thing you can do to improve your work-life with a chronic illness/disability is to find a great manager. The company that laided me off only did it after my manager changed away from the person I actually interviewed with. Remote work is generally easier to keep your illness from being noticeable to as many people.
And while it is illegal for your workplace to do all sorts of things, they will still do it. Suing a current/former employer is a nuclear option that will likely hurt you far more than it could ever help you. They can always get retribution every time a future employer calls to confirm previous employment.
It's been 5 years now, and I still feel guilty about not suing Intuit over my entire experience there. Not because I needed the attention, money, drama, etc. Just because I know they continued doing it to more people like me after I left.
As a more practical matter, I've found it really important to be smart about when I change/add/remove my prescriptions. If you take enough drugs, there will be bad side-effects, and you don't want to have it happen on the day of your annual review (speaking from experience), big presentation, etc.
This has been my experience, as well. I only gave that advice because I know of several people who wear their conditions on their sleeve and are successful doing so, however it's certainly not the path I would choose for myself. I agree with the rest of your post, as well.
I'd be careful of this approach if there is something like a company rule that all accommodations must go through HR.
You sound like a manager who actually cares and empathizes with your employee. I had a manager like you. It was amazing. But you aren't the norm.
Going to HR will generally only draw negative attention. There is no situation I've seen where someone needed HR and HR actually did anything meaningful to support them.
I prefer to deal with each manager differently. Getting it in your HR file means you lose control over who knows what, and how it was explained to them.
If it becomes apparent that $CURRENT_EMPLOYER is not such a place, it's time to start protecting yourself with things like formal disability accommodations through HR, etc. The problem is that once this becomes apparent, shrewd politicians will have already worked to make it look like your accommodations are just a cover-up. That's not necessarily a deal killer, as every company puts a different weight on the legal risk that HR exists to prevent, but it's not likely to ingratiate your manager, which makes things difficult.
The long and short of it is that it's folly to imagine that HR is in your corner. They are paid by the company and they exist to keep the company free from the mind-boggling expense of lawsuits. You can work this to your advantage sometimes.
I’m sure this varies around the world and exactly what this looks like in practice isn’t simple. Here in NZ, if the illness has the potential to impact on your work I believe you need to disclose it.
I recommend not going into specifics about your condition if you choose to say anything at all about it. You will come across people who will have opinions about it, despite not having to live with it.
Also, be aware that it is illegal for your workplace to pry about your health if you don't want to disclose specifics.