I've read somewhere that above 2500 meters (8,202 ft) 20% of climbers report having had altitude sickness. IIRC they also wrote that 40% of climbers report altitude sickness above 3500 meters (11,500 ft) though I'm unsure about the latter value. I wonder at what altitude the percentage approaches 50% and more. Preferrably in mid-latitude mountains (such as the Alps, the New Zealand Southern Alps, the Cascade range, northern Colorado or the Caucasus) because at the mid-latitudes the atmospheric pressure at an elevation should be about the same as at the pressure altitude on an aircraft's altimeter. Answer may include values from high altitude chambers.
It's not definable to the level of precision you seem to be imagining, but probably somewhere around 16,000' (~4,900 meters). It depends on what criteria you use. For some references, see the introductory section of this paper: Dallimore, J., & Rowbotham, E. C. (2009). Incidence of Acute Mountain Sickness in Adolescents. Wilderness & Environmental Medicine, 20(3), 221–224. doi:10.1580/07-weme-or-119r3.1 https://sci-hub.se/10.1580/07-WEME-OR-119R3.1
There is a background rate of something like 10%, which is just because people often feel bad while they're in the mountains because of factors like lack of sleep, caffeine withdrawal, and so on: https://pubmed.ncbi.nlm.nih.gov/22441083/