I'm afraid I don't have the answer. It looks to me like a problem in the version of TLS available (perhaps you don't have the latest version of RCurl?).
One thing you can try is the package httr which sometimes works better. Something along these lines:
library(httr)
GET("https://impi.corp.zy.com/internal_data/api/fet/AReco?Date(s)=2020-08-02&Response%20Type=csv&Async=false",
add_headers(c(Accept = "application/json",
Authorization = "5c81-e875-48f7-98-ee78")))