As a disclaimer, I'm a big proponent of outsiders contributing to unrelated fields and do so myself as an archaeologist in tech. The way to do it is not by ignoring prior work done in the field, but instead by engaging with it constructively. These authors haven't really done that and it shows in the quality of this paper.
While the 'impact' hypothesis is certainly unsettled, there isn't much controversy in the hard sciences. The great majority of over 200 papers published in the last dozen years certainly establishes the presence and dating of fallout from major (probably multiple) extra-terrestrial sources in that era. That evidence is in accordance with multiple Greenland ice-cores.
Whatever the purpose of Gobekli, it's only one data point in a long and growing list of recent discoveries and observations. Human history in the early Holocene will be re-written as a result.
If there is so much smoke there's gotta be fire.
If you look at last glacial maximum, sea-levels were 110-120m below where they are today. They rose from below 100m to 0m in a matter of only about 8000 years (13000 BC to 5000 BC) . Persian gulf region was fertile land, got flooded and turned into a gulf. The sea-level rise was observed/experienced all over the world.
At one point the sea-level rise was so fast it was 2-3m in one lifetime. This much vertical change in coastal regions can change the landscape by 100s of meters horizontally. So you could be living in that time and hearing stories from your grandfather about the vast amount of land that got flooded over his lifetime.
Word-of-mouth "history became legend. Legend became myth" (to quote LOTR).
Written history did not start until much later (Gilgamesh ~2100BC, Herodotus ~450BC, neither considered serious/rigorous historical works. I guess Gilgamesh is considered fiction.).
I think it's a highly valid theory that sea-level rise led to flood myths in so many regions and so many religions all over the world.
Australian oral traditions record social upheavals when people moving out of the flooded Sahul region (between present Australia and New Guinea) had to negotiate shared use of the high ground that had already been populated for at least 40,000 y. It seems a safe guess that it would be traumatic to have to leave an area your people have lived in for tens of millennia.
Aboriginal Memories of Inundation of the
Australian Coast Dating from More than 7000
Patrick D. Nunn & Nicholas J. Reid, 2015
We have certain knowledge that the Amazon region was heavily cultivated ~10,000ya, which would have required substantial population. A lot can happen in a millennium or three.
Also, there is evidence of multiple extinctions in South America and South Africa at the same time, and of a strike in Syria. I don't think we have evidence yet to determine a bound on the range of effects.
We don't know all that much about the supposed impact, as you say. Just that more large mammals in North America went extinct than anywhere else, so it was likely the worst affected.
During the last deglaciation that followed the end of the Last Glacial Maximum, geologists estimate that a cycle of flooding and reformation of the lake lasted an average of 55 years and that the floods occurred several times over the 2,000-year period between 15,000 and 13,000 years ago. U.S. Geological Survey hydrologist Jim O'Connor and Spanish Center of Environmental Studies scientist Gerard Benito have found evidence of at least twenty-five massive floods, the largest discharging about 10 cubic kilometers per hour (2.7 million m³/s, 13 times the Amazon River).
While fast in a geological sense, I do not think it is fast enough to inspire all those myths of catastrophic and sudden floods.