Wasn't "just" a 10 ga extension but also a 20A fuse or circuit breaker. 12 gauge is OK but 14ga may get hot.
The issue is not so much the run current (11-12A) but the 60A starting surge for a stock AC (for more than you ever wanted to know, see
here ). It only lasts for a few milliseconds but will usually pop a 15A (most home outlet wiring is 14GA and with a 15A breaker). When I had my back garage built the outlet wiring was all 10 GA on 20A breakers. Also paid $200 extra for all copper wiring when I had the house built- no aluminum.
Have been trying to decide what to do now that am retired. One possibility has been a properly engineered power system for travel trailers that includes dry camping with AC. Suspect there are others who would like their AC to run reliably on a Honda EU2000i, the standard of the travel world. (AC and coffee takes a little more grunt).