As long as you meet the conditions you hold the rights whether or not you make any form of application. You will be able to apply for a residence document to prove you are protected under the Withdrawal Agreement (and would be advised to do so).
GOOD NEWS DAY
It’s official Greece has chosen the declaratory system In a nutshell this is going to make our transition to biometric a lot easier. All we have to do now is make sure everyone is registered by 31/12. https://ec.europa.eu/info/sites/info/files/brexit_files/info_site/overview_ms_residence_rights.pdf
The 2nd BiE explainer (in Announcements) has this to say about the declaratory system
What does this mean for us?
Provided we are registered as resident in Greece by 31/12 (beige or blue) we are not obliged to make any further application to secure our rights. The acquisition of the new permits should be optional and we can’t be refused one unless we are deemed a security risk.
There should be no deadline for the new permits.
We will have to wait for the Greek legislation for this level of detail but it’s looking very good
source – FB post British in Greece