There's real research on this. Shu pu-erh specifically has been studied for lipid metabolism effects — the fermentation process produces unique microbiota that appear to assist with fat breakdown. A 2011 study in the Journal of Agricultural and Food Chemistry showed reduced plasma cholesterol in rats. Human studies are smaller but directionally consistent. Practically speaking: it's not magic weight loss tea, but drinking it after fatty meals instead of nothing does seem to help digestion for most people.
Shu and sheng work differently here. Shu (ripe) has the fermented microorganisms that are linked to the digestion effects. Sheng (raw) is more like a fresh/aged green tea — it has caffeine and catechins which stimulate digestion differently but less specifically. For post-meal digestion, shu is the traditional and likely more effective choice.
Anecdotally — I drink shu every day after lunch and my digestion is noticeably better than when I skip it. Could be correlation but after 6 months the pattern is consistent enough that I don't bother testing the alternative.
