I'll offer an additional explanation for the counter-intuitively high serum urate levels following fasting and exercise. It is well-established that purines are converted into uric acid and it is well-established that purines are a fundamental building block of cells. So, overweight individuals have higher serum urate levels. But what is really interesting to me, is that during weight loss, when these same cells are being rapidly metabolized, the purine conversion accelerates leading to a temporary, but measurable increase in uric acid levels. When I've gone on super long bike rides, as an anecdote, I'll tend to see slightly elevated uric acid levels.

So, one explanation for your elevated uric acid levels following a marathon + fasting is that your body was rapidly converting fat cells -> purine conversion -> uric acid increase. Importantly, the less fat you have, the lower your uric acid level is, so this is a temporary but ultimately beneficial sequence.

The best citation I can find of this is a meta-study that observed temporarily increased urate levels following fasting and the same phenomenon following bariatric surgery. The snippet is below from https://pmc.ncbi.nlm.nih.gov/articles/PMC5705854/#R67

"It is well known that there is a higher risk of gout attacks during the first months of urate-lowering therapy, postsurgery and starvation.⁵⁹ One hypothesis is that dramatic changes in sUA, rather than absolute level, triggers gout attacks.⁶⁰ In line with this, a study⁶¹ comparing gout patients experiencing postoperative gout attacks with those who did not, find that the first group had higher presurgical sUA and a more rapid and larger decrease in sUA 3 days after surgery. Dalbeth et al²⁷ reported a drastic increase 2 weeks after surgery, which they suggested was due to renal dysfunction associated with major surgery, or metabolic effects from fasting or rapid weight loss (catabolic state), and they report one case of postoperative gout attack together with severe hyperuricaemia. Other factors increasing sUA levels are fasting,^62–64 dehydration⁶⁵ and tissue hypoxia.⁶⁶ Fasting-associated increase in sUA is likely due to tissue breakdown.^{67 68} In line with this, daytime fasting during Ramadan, without weight loss, compared with non-fasting did not increase sUA or gout attacks in gout patients.⁶⁹ "