Since zsh is officially macOS's default shell, I'll focus on it. So I just installed Miniconda, and added ~/miniconda3/bin to my PATH. Click the option it adds and it will create a symbolic link to the selected file or folder in the current directory. What “conda init” does is to set up a conda “shell function” and keep the other stuff off PATH.
“Modifying PATH can cause problems if there are any other programs on your system that have the same names, that Anaconda then hides (shadows) by being found first.