curl error:1400442e:ssl routines:connect_cr_srvr_hello:tlsv1 alert protocol version

Run the following:

export HOMEBREW_FORCE_BREWED_CURL=1
# check that the Curl: entry now points to Homebrew curl
brew config
brew install package-name

brew is probably sticking with your system curl because it's not old enough to reject outright, but it is old enough to maybe have problems connecting with some sites.