The sense inventory in ODE is a reorganized version of the one in NODE/DIMAP. Both sources have sixteen senses that do not entirely correspond. I have used the ODE inventory, as usual.
Notes from the spreadsheets:
Under has its own spreadsheet since there are so many senses; it is incorporated in toto into the Sense Analysis Summary. No new senses were added.
Other instances of under that may deserve idiomatic treatment
ODE has “under way” which is not too far removed from sense 14(5) but is easily isolatable as an unvarying expression, and in fact is often spelled “underway” in American English and identified as an adjective in US dictionaries.
“out from under X” is a common phrase that might be treated at any of its components, though it is not in ODE at any of them. Possibly it can be parsed as an under PP (and in most cases it would fall easily under sense 8(4) or one of the first 3 “literal” senses), with out as adverbial, and from a sort of superpreposition which has the under PP as its complement.
Under figures in dozens of English idioms in which it usually corresponds to a defined sense, though the idiom as a whole does not parse literally (e.g., “hot under the collar”, “under the gun”). See, e.g., NTC’s American Idioms Dictionary index for a representative list.
The idiom “under one’s breath” doesn’t fit any defined sense of under. I have classified the two instances occurring in FN as sense 14(5), as the closest fit.