There isn't anything new here. Some tickets won't offer this button since they are not upgradeable via Self Serve (e.g. corporate tickets, foreign currency). All this button does is lead you to the same back-end of BA.com, and right at the bottom you will see the Upgrade options for cash or Avios in the normal way. If you are in Self Serve then in theory a fare difference upgrade should show, which unless your ticket was booked in a high fare bucket will be expensive.

And obviously if you were not using the App but BA.com MMB instead then you'd be in exactly the same place.

If either a POUG or an AppUp was showing (see Dashboard) then you don't get the blue star button, instead you get the Limited Time offer button, images in the threads referenced. That may be more interesting. And BA.com MMB will also show the same sort of thing, but the Limited Time aspect is a little easier to spot due to the rolling banner at the top.

I'm not aware of any substantial changes in this area in the last year, other than that BA have made some efforts to keep more bookings in Self Serve. If you are not in Self Serve you can still get a fare difference change, it just needs a call to the Contact Centre or Ticketing Agent at the airport to do the calculations. Or you could use tools such as ITA Matrix / ExpertFlyer to work it out for yourself.