"replicate an entirely new, healthy organ for replacement"
It literally states they replicated an entirely new healthy organ...
And I'm literally stating that they're using biological replication, not technological molecular replication, because if they were using technological molecular replication they'd have no need to specifically call out the need to scan patient DNA.
Ah, good, "neural energy". Glad we cleared that up and went with something sensible.You're mixing up the halves from "Our Man Bashir".
ROM: Neural energy has to be stored at the quantum level. The holosuite can't handle that.
ODO: So if their physical bodies are stored here, where are their brain patterns?
QUARK: Everywhere else. Their brain patterns are so large that they're taking up every bit of computer memory on the station. Replicator memory, weapons, life supports.
It was specifically the neural energy that had to be stored at a quantum level, and also that was the crappy Cardasian computers, not Starfleet computers. Which we know from 11001001 are capable of a lot higher level of storage.
All we know from TNG: "11001001" is that in 2364 the Enterprise-D (and possibly the other few Galaxy-class ships around at the time) had the largest and most powerful mobile computers in the Federation. It tells us nothing about how effective Cardassian computers were, because the Bynars weren't members of the Cardassian Union; and we might imply from "11001001" that space stations can have significantly more complex and powerful computers than starships. And even assuming Cardassian computers were less powerful than the Starfleet equivalents, why would Starfleet have not upgraded them by DS9: "Our Man Bashir" after running the station for four years? They upgraded the weapons and shields.