This post reminds me of the words of Vernor Vinge:
"A mind that stays at the same capacity cannot live forever; after a few thousand years it would look more like a repeating tape loop than a person. To live indefinitely long, the mind itself must grow ... and when it becomes great enough, and looks back ... what fellow-feeling can it have with the soul that it was originally?
Transhumanism also involves growth, you don't touch this aspect in your post.
growth is irrelevant in eternity.
Why? Things could grow and change eternally. And there might be no eternity, compared to the human scale yes, but absolutely maybe not.
We wouldn't be any different than a rock at that point. we would be indifferent to anything.
Yes, like the Troglodytes in Borges "The Immortal". But I don't see the connection to the discussion we started here. Your (and Borges) thoughts assume immortality without growth.
There can't be any growth as some point. The periodic table of elements only has that many elements and only a few combinations can be made in an infinite time.
But then you also have to consider that the universe will not be inhabitable indefinitely, the entropy is growing, the hydrogen necessary for nuclear fusion in the stars will be depleted at some point and so on. Once we leave the human time scale this has to be taken into account. There is some question what can happen in the limit. Altogether I think that it is an interesting thought experiment of you (and Borges), but it cannot serve, at least in this simple form, as refutation of transhumanism.