I feel fairly certain that Blue Origin has plans for second stage reuse. Whether these plans have gone much past the napkin phase is another question.

SpaceX mocked up a plan to reuse the second stage of Falcon 9. https://www.youtube.com/watch?v=sSF81yjVbJE These plans were scrapped to concentrate on Starship.

If the Falcon 9 is big enough to have enough margin to support second stage reuse, New Glenn definitely does too.

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.

It’s amazing that Blue Origin is older than SpaceX.

Granted for much of its history it was a science project. Blue was tiny for most of its history.

The push to scale up and become an operational launch company has only ramped up in the past several years.

They still move somewhat slowly and are fiercely private, but those early years were targeting different goals.