You forgot to import Arduino's public key to the temporary keyring prior to performing the verification. The key import is only effective while that temporary keyring is in use, so you will need to repeat the import if GPG_HOME has changed (it changes each time you run the GPG_HOME="$(mktemp --directory -t gpg-temp-home-XXXXXX)" command), or if your operating system has clears the contents of your system's temporary folder (which is where the temporary keyring is stored).
So run this command to import the public key:
gpg --homedir "$GPG_HOME" --import /tmp/arduino_public.gpg.key
then try the verification once again.
Since the public key file was downloaded to the temporary folder, it is possible your operating system already deleted it. If so, you will need to download the key file once again before running the import command: