Permanently change zsh environment variable on macOS Big Sur?
Undo whatever changes you made to /etc/zshrc, then forget that this file exists. You should be leaving that file alone.
Put your changes in $HOME/.zshrc. This will usually work, zsh should read that file on startup whenever the shell is an interactive one (see man zsh). Note that zsh reads that file regardless of whether or not it is a login shell, so it will be interpreted on every shell invocation.
Forget that sudo exists.