My guess:
Apple knows that 128gb "almost-iPhone-16" for <$500 could ruin the the iPhone 16 sales, so I think they might:
a) launch 64gb version as the base for $500 and 256gb version for $650 (no 128gb version = classic Apple)
b) the rebrand could justify much bigger price increase to like $600-650, because it's no longer the SE + keep the current SE as the base model. Would be nice if they at least gave it USB-C, so it could return to Europe.
I'm still not sure about the 16E name. Does it mean they are going to launch a new one every year? The SE name is more practical for a device that is not refreshed every year.