I've thought about getting a Greek passport. However, after weighing the pros and cons, I decided it wasn't worth it. The main Con is that you'll need to deal w/ the Greek government and that is a nightmare. If you've never had that pleasure, try something simple while in Greece. Go to the local police station and ask about getting an extension on your Schengen visa. They will direct you to another office, which will then direct you to another office, and so on. This can go on for several days until you find someone who actually takes the time to help. Otherwise, everyone you meet will scream at you as if you've committed a crime and tell you to go back to the office you just came from. Nobody knows the answer, but they all act like they do ... and it's always coffee break time, so "please come back later!" This is a country where they pay public employees a bonus just for showing up on time. The main reason I decided not to get a Greek passport is b/c I'm not really Greek. I didn't grow up there. So, I don't know the laws. I don't want to be stopped at the airport b/c there's suddenly a new banana-republic tax I didn't know about, or they decided to restrict access to ATMs, etc.
Instead of a Greek passport, you may want to look into a Financially Independent Persons residency program visa if you were planning to live there. This page describes the requirements -
https://greekresidency.com/golden-visa/fip-residency-for-financially-independent/.