Austria also has the information available here in English:
https://www.austria.info/en/service-...us-information
According to this, if you are Greek or a resident of Greece, you would not need a COVID test to enter Austria:
At the moment, travellers from the following countries do not need to show a negative COVID-19 test or commit to quarantine: Belgium, Germany, Denmark (including the Faroe Islands), Estonia, Finland, France, Greece, Iceland, Italy, Latvia, Liechtenstein, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Switzerland, Slovakia, Slovenia, Czech Republic, Hungary, Croatia, Ireland, Cyprus, Andorra, Monaco, San Marino, Vatican City, Spain.
The regulation applies only to people who are residents in the listed countries or Austrian citizens. It is also a prerequisite that you have not been in any country other than Austria or those European countries in the past 14 days.