Right; I have no doubt that Blue/people inside of Blue are having serious thoughts about 2nd stage re-use, at least to a level roughly equivalent to what you pointed out SpaceX has revealed.

However, I suspect 2nd stage/full re-use is fundamentally so much harder than 'just' 1st stage re-use that it requires a full re-use design from top to bottom, a la Starship/Superheavy.

Of course, Blue has been historically far more closed than SpaceX, so it's possible that they have legit, in progress full re-use! That would be great.

The second stage of New Glenn runs on liquid oxygen and hydrogen, not on liquid oxygen and RP-1 as Falcon. It makes it much harder to reuse simply due to much bigger fuel tanks and significantly less tolerance to overheating . I doubt Blue Origin really considers that seriously.

I guess it depends on what you call a redesign. They likely need to modify the fins to counter act any new control authority on the upper stage, but other than that I see no reason why the first stage would change.