You can't escape the fact that before Brexit, as an EU member country but not part of Schengen, UK citizens were subject to Schengen border checks, i.e. passport control, BUT NOT to Schengen rules. Now, as a third country, UK citizens are subject to both Schengen border checks and Schengen rules. The only exception to this are people who were resident in an EU member state before the UK finally left the EU, since they come under the terms of the Withdrawal Agreement which allows them to maintain there residency rights. The Withdrawal Agreement made no special provision for people who weren't, or did not want to be, resident in an EU member state but wished to still come and go as they pleased. No such category exists within the Withdrawal Agreement or within Schengen rules. It is possible that national rules may permit different terms of entry for specific classes of individuals but as far as I can see they are pretty limited and don't really fit what some people want to do.
People who held a beige residence certificate before the UK finally left the EU, because they wished to be in Greece for more than 3 months but less than 6 months in each year can still apply for the new biometric card without any problems. Those who never got a residence certificate but can show prior residency by other means can also apply for the new biometric residence card, although they may need to jump through a few more hoops. People should think carefully before doing so, however. By applying for the biometric residence card they are legally declaring to Greece's immigration department that, at least going forward, they are permanently resident in Greece, i.e. for over 183 days in each year. That might create problems at some time in the future if they are also legally declaring to another Greek government department, e.g. the tax office, that they are not resident in Greece for over 183 days in each year. I don't know if such problems will occur and I offer no advice whatsoever but logically they are a possibility and so should be considered before deciding what to do.