Looking at the warning which you added in your question, I surmise that nvm is installed on your machine but may not have been setup properly. Nevertheless, adding full steps for you to verify which one you missed and fix the same.

1. Confirm nvm is installed

Before making changes, check if nvm exists:

# confirm nvm is installed
$ brew list | grep nvm
# if the above doesn't return anything, install nvm
$ brew install nvm

2. Ensure your system is in good shape

Sometimes Homebrew issues prevent nvm from working properly. For that run:

$ brew doctor
# If you see any warnings, follow the suggested fixes and 
# rerun brew doctor until everything looks good. 

3. Create the nvm directory (if missing)

$ mkdir -p ~/.nvm

4. Add nvm to your shell configuration

Manually add these lines to ~/.zshrc:

export NVM_DIR="$HOME/.nvm"
[ -s "$(brew --prefix nvm)/nvm.sh" ] && . "$(brew --prefix nvm)/nvm.sh"
[ -s "$(brew --prefix nvm)/etc/bash_completion.d/nvm" ] && . "$(brew --prefix nvm)/etc/bash_completion.d/nvm"

Save the file and reload the configuration:

$ source ~/.zshrc

5. Verify and Restart

Check if nvm is now working:

$ nvm -v

If you still get an error, restart your terminal and try again. Sometimes failing to do this might also lead to issues.