Rather than message saying download latest eBay app and sign-in to account, think receiving url for this "new" eBay app should be only when signed in to account. Message instructions say, go to "my eBay>settings>signing-in>2-step verification>then verify 2-step verification". That's not exactly how I see things in my eBay interface.
My current 2-step is functioning ok as far as I see. I would not download this "new" eBay app until the process appears 100% kosher. Many phishing schemes on internet. ebay ought to have made any upgrade procedure appear completely legit.