Actually it kinda did. The part where he said "too bad you only have one lifetime."
For me, it implies that Brain and Luxu made a deal of some sorts, where he was ends up in the future Scala and Luxu (not sure if that's he's actual face) looking like Brain. (Tbh looks a lot like Zexion)
Btw, I'm not sure but do they ever explain where little Zexion came from? All I can find is that he was an orphan and I'm like, that's a bit suspicious if you ask me.
I'm inclined to believe as well that Luxu and Brain came to some sort of agreement.
The way Luxu words it seems to indicate that he thinks losing Brain's intellect by having him stuck in the crumbling world would be a waste so while he might indeed take Brain's
body as his first vessel and yeeted Brain's
heart out like Ansem SoD did in KH 1 with Riku and Master Xehanort
attempted in BBS with Terra he did not do so aimlessly but actually flung Brain's heart into the future using his own powers.
Maybe Luxu even bestowed the No Name to Brain and "stored" it somehow inside his heart to send it with him, similar to how Aqua sent her Keyblade (with her armor) with Terra-Xehanort in an attempt to save Terra at the end of Final Episode.
What exactly caused Brain to regain a physical form in Scala ad Caelum during the time of Sigurd is another matter that can't yet be fully made sense of, but considering that
only hearts can travel through time I think it is safe to assume that the "body" or vessel Brain inhabits in that scene does not have to be, or rather
can't be the original body he resided in during the era of Daybreak Town where the meeting with Luxu took place simply because he couldn't have taken it with him.
So Luxu inhabiting the original body would not mean the end for Brain nor does it have to mean that Brain's heart would be a captive in its own body because Luxu took over.
That Xehanort did this with Terra is only "Nort style" and does not have to be the case with all Keyblade Masters who use the heart transfer technique.
Of course, there's
also the possibility that Brain escaped via Luxu's own variant of foregoing the end of the world and their hearts actually
share one body, not unlike Sora did with Ventus' and later Roxas' and Xion's hearts.
The difference would be that they either take turns in controlling the body in agreement with each other depending on who has an urgent task to do
or Luxu's heart simply stays inside Brain doing his role of
watching through his willing host's eyes without actively exercising control.