As far as you already applied to the competent immigration office, a blue paper is issued, which is your temporary residency permit. With this paper you can stay in Greece.
How can I stay in Greece while waiting for my residency permit to be processed?
I entered Greece with a type C Schengen visa at the end of this May. I purchased a property and filed the Golden Visa application last week. My 90-day stay period through my type C visa is almost over but I still have unfinished work to do on my new property. Is there any way that I could stay beyond the 90-day restriction while the application is being processed? I prefer not to leave the country and apply for a different kind of visa.
Ιn accordance with the applicable procedures for the issuance of a permanent residency permit for property owners, when the file with the supporting documents is submitted either personally or through your legal representative upon POA, a check of the submitted documents is being concluded and a temporary residency permit (blue card) is issued for one year. This kind of residency permit grants the investor the right either to live permanently in the country or enter in the country legally without the need of another type visa until the issuance of the permanent one. Also, the investor is required either on the day of filing or within six months to attend to the competent authorities to provide biometrics. Based on the above, and since you have received the temporary residency permit, you have no problem with your presence in the country.