I meet the same problem, but I found it nothing to do with nginx. I am using nodejs as backend server, use nginx as a reverse proxy, 413 code is triggered by node server. node use koa parse the body. koa limit the urlencoded length.
formLimit: limit of the urlencoded body. If the body ends up being larger than this limit, a 413 error code is returned. Default is 56kb.
set formLimit to bigger can solve this problem.