This is a good question that I am only partially qualified to answer, mainly because I have looked into it in some depth. A full answer can be given by a medical professional with actual working experience in high altitude - this is a very small group of researchers or some medics from the Indian/Chinese armies. That being said,
First of all, 6000M is not that high and certainly not extreme. So let's talk about 8000M.
From the first paper you linked to
Only 1 in 13 of the Everest climbers had a normal MRI; the amateur showed frontal subcortical lesions, and the remainder had cortical atrophy and enlargement of Virchow-Robin spaces but no lesions. Among the remaining amateurs, 13 showed symptoms of high-altitude illness, 5 had subcortical irreversible lesions, and 10 had innumerable widened Virchow-Robin spaces. Conversely, we did not see any lesion in the control group. We found no significant differences in the metabolite ratios between climbers and control
So Fayed et al concluded that
We conclude that there is enough evidence of brain damage after high altitude climbing; the amateur climbers seem to be at higher risk of suffering brain damage than professional climbers.
The second paper you linked to doesn't actually consider "high altitude". Fan et al are looking at the Tibet plateau, which is around 4500M in elevation and there are humans living there all year round (nomadic tribes and Chinese soldiers). Not surprisingly, the physiological effects are less pronounced.
The BoulderWeekly article states
Of the 12 professional climbers and one amateur in the Everest expeditionary group, 11 climbers’ MRIs indicated evidence of brain atrophy, a decrease in the size of the brain, and the enlargement of fluid spaces surrounding the brain vasculature.
and further on
Only the amateur’s image indicated brain lesions after suffering symptoms consistent with acute mountain sickness (AMS) and high altitude pulmonary edema (HAPE). One professional mountaineer’s image demonstrated normal MRI results with no atrophy or lesions.
So I understand that as everyone suffers from brain atrophy while only amateurs (climbers who are not acclimatized) suffer from irreversible lesions.
The Kotke paper concludes
A single sojourn to extreme altitudes is not associated with development of focal white matter hyperintensities and grey matter atrophy but leads to a decrease in brain white matter fraction. Microhemorrhages indicative of substantial blood-brain barrier disruption occur in a significant number of climbers attaining extreme altitudes.
Again - consistent with atrophy in all cases. And lesions in some.
Additionally, you must consider the work of John B. West, who has been working in high altitude medicine for many decades now. From this paper
Impairment was manifest by deficits in memory storage and recall, aphasia, concentration, and finger tapping speed; the last deficit was still detectable a year later in one group of mountaineers.
From this other paper by the same author
However, there is impairment of central nervous system function at high altitude which persists following return to sea level. Significant abnormalities of motor coordination persisted for more than 12 months in most members of the Everest expedition
There is evidence that the climbers who ventilate most at high altitude have the most central nervous system impairment, presumably because of the more severe cerebral vasoconstriction.
So this probably answers your question. There are long term effects in all cases. Amateurs (unacclimatized climbers) suffer the most.
However, there are many examples of mountaineers coming back to live normal successful professional lives. So how severe the long term after effects are is something that varies.
You could also consider people who have done Mt Everest without supplemental Oxygen and find out how they are doing. (Reinhold Messer few decades back to Adrian Ballinger more recently). Afaik, Ballinger is still active in his profession though Messner is retired after a long career post-Everest.
But would e.g. Kilimanjaro or Nepali or Andean trekking peaks in the 5000-6000m range also risk permanent damage?
No, it would not. Your SpO2 will reduce while you are at that altitude; AMS, sure it is common, but nothing long term. Hundreds of people do 6000M peaks in India/Pakistan/China/Nepal with no long term brain effects. Very rarely do people suffer from cerebral edema at these altitudes, but it happens, and that's a bigger risk you should be aware of. However, edema doesn't onset suddenly, so as long as you are aware of symptoms, and start to descend at the right time, you'll be fine.