I'm trying to download my own voice message (my recorded greeting) from Google Voice. Is there an option to do it?
Yes, use the Google Takeout service to download your Google Voice data.
This is what the Google Voice archive will contain:
Your Voice billing history and conversations will be provided as HTML. Greetings and voicemail recordings will be provided as MPEG Audio (mp3). Your list of phones will be provided in the vCard format.