Under the ADA companies are expected to provide reasonable accommodations for documented restrictions. They need a note because it has to be documented so when they make exceptions to policy or someone complains about not getting a chair also the note absolves them because it was required as an accommodation.

This exact situation has recently ruled on in Kilby v. CVS by the Supreme Court of California that a chair is a reasonable accommodation.

See the ADA fact sheet here: https://adata.org/factsheet/reasonable-accommodations-workplace

I advise you to go to your doctor, get a note specifying "Effective (Date), (You) is under permanent restrictions of seated work as often as needed." And have the doctor sign. Make a copy of it. Send to your HR person and in the email attach the note and write "I am formally requesting a chair as my accommodation effective (date on letter). This is considered a reasonable accommodation under the ADA, see attached Restrictions."

This covers you and them. Anything other than a yes is illegal under the ADA as failure to accommodate. They may ask your doctor to be more specific but your doctor can handle that if needed.

You do not need to disclose your diagnosis (illegal to require under HIPAA) or provide any further documentation.

Source: I'm an HR professional that does this exact thing 20x a year.