Nobody knows exactly what the two-year cap would look like in practice because right now it’s purely hypothetical. Without being familiar with your specific case, I’m guessing that you’re currently handing in SSD info for income verification purposes, not as part of ensuring that you meet some qualification for participation in the program.
“Disabled” within the context of Section 8 doesn’t necessarily mean much in and of itself. It can qualify you for a Mainstream, or NED voucher, if you’re disabled and under the age of 62. Those function exactly like a Housing Choice Voucher but they’re funded differently. Being disabled or over 62 can also qualify you for certain public housing developments that would otherwise be inaccessible. Aside from that, being elderly or disabled does not currently affect eligibility in any way.
To address what you found on the internet: if you were to need to verify disabled status for HUD, in my experience any documentation that you were required to produce in order to get SSD in the first place would be more than sufficient to establish you as disabled for HUD’s purposes.