Well lots of gene lines were wiped out perhaps that may have had some Neanderthal in them is what I was thinking.
As I recall, the Toba thing essentially triggered one of the Ice Ages. We see in sites in the Near East that at different times both Neanderthals and archaic sapiens species were present. The key is "different times." It looks like they actually had somewhat different ecological zones where the Neanderthals were more cold-adapted. So, when it got colder,
everybody shifted south and then, when that passed,
everybody shifted north.
You have to imagine that, if the sapiens group was being bottlenecked, the Neanderthals were feeling the pain somewhat too. But maybe not as much. In the study you linked, Neanderthals came out ahead of moderns in diversity.
So my bottom line is ... I don't know.