I've been playing around with keyboard scrolling of overflow regions, and I was interested to note how Firefox's native behavior doesn't expose any additional semantics -- i.e., it doesn't apply a role or accessible name when the scrolling region becomes focusable.
And I think that's the right thing to do -- that our standard workaround of including role="region" and aria-label or aria-labelledby (along with tabindex="0") creates unnecessary verbosity.
I've created a demo script on that basis, which doesn't add a role or label, it simply adds or removes tabindex based on whether the region actually has overflowing content.
It's triggered by a ResizeObserver so it continually updates in response to anything that changes the element's size (and you can test this by resizing the window, increasing zoom or font-size).