Answers
You cannot work, but you can be the shareholder of the company and manage your company. There is a type of work permit through business investments that allows you to work in Greece - the Strategic Investment category - but you must make a big investment
Your residence permit does not give you access to the labour market. But the holders of such a residence permit(investors) have access to the exercise of the investment activities as a legal representative, a president, a board member or a chief executive officer. The executives of the investment have access to dependent employment for the needs of the investment.
As a holder of the Greek golden visa, you have the right to establish your own company in Greece and at the same time to be the legal representative of this company. You don’t have any other right to work as an employee of the company.
In the case that you set up a business, you could run it.