There is a system-wide /etc/profile or /etc/profile.d/
Likewise, zsh will look for /etc/zshrc
And zsh will actually look at
$ZDOTDIR/.zshenv
$ZDOTDIR/.zprofile
$ZDOTDIR/.zshrc
$ZDOTDIR/.zlogin
$ZDOTDIR/.zlogout
So perhaps you can set the value of ZDOTDIR in one of the systemwide locations to use "$HOME/foo/bar/zsh/" and this way zsh will use ~/foo/bar/zsh/ as the location for the user specific .zshrc and other mentioned files for every user
https://eng.libretexts.org/Bookshelves/Computer_Science/Oper...
https://bash.cyberciti.biz/guide/Setting_system_wide_shell_o...
https://zsh.sourceforge.io/Intro/intro_3.html