As you say, with the Golden Visa neither you nor your wife has the right to work. But, if you or your wife applies for a working permit under a specific legal status and receives a permit, there is no impact on the status of your Golden Visa. You need to get advice on how to proceed with the working permit.
How can I hire my wife in the business I establish in Greece without jeopardizing our residency status?
My wife and I obtained our Greek Golden Visas. I was told that I could work in the capacity of a shareholder for a company I set up. If I establish a company and stay compliant with Greek employment law, can I sponsor my wife for a work permit and hire her to legally work for me? Will this impact our status as Golden Visa holders?
She cannot work with the resident permit of a Golden Visa dependent person. She can be a shareholder too or ask for a national visa from the Greek embassy under specific requirements, e.g., your company here to be a branch of a foreign company, etc.
According to the law, in no case does the resident permit for property owners provide access to any type of employment. Employment, according to paragraph 6, article 20, of Law 4251/2014, does not include the exercise of economic activity in the capacity of a shareholder or a chief executive officer for an already existing company. The family members who have been issued a resident permit for the same duration as the sponsor are similarly not granted access to the employment market. So, you have the right to ask economic activity, under the above roles in a company, already existing, and your wife does not have access to employment market.