oh boy... -b takes an option which in your examples is -A and -e, then what follows is interpreted as a URL and you throw away the warnings:

  % curl -vgsSIw'> %{time_total}\n' -b -A "curl/8.2.1" https://t.co/DzIiCFp7Ti 2>&1 | grep '^\(* WARNING: \)\|\(Could not resolve host: \)\|>' 
  * WARNING: failed to open cookie file "-A"
  * Could not resolve host: curl
  curl: (6) Could not resolve host: curl
  * WARNING: failed to open cookie file "-A"
  > HEAD /DzIiCFp7Ti HTTP/2
  > Host: t.co
  > User-Agent: curl/8.1.2
  > Accept: */*
  > 
  > 0.013309
  > 0.112494