Under the Withdrawal Agreement, if you already have a Permanent Residence Certificate it should simply be exchanged for the new Biometric Residence Card, possibly subject to a criminal record check.
If you have the Initial Residence Certificate, i.e you have not satisfied the 5 year qualification period for a permanent one, then you will be expected to produce proof that you still satisfy one of the conditions under which an initial Residence Certificate is issued. For most of us that will mean proof of where you live, e.g. deeds or a rental agreement, proof of income, e.g. Greek tax clearance form, bank book or P60, and proof of medical insurance, e.g. IKA book/certificate or private medical insurance policy. It is possible but not certain that an EHIC might be accepted.
I think there is some misunderstanding about requirements because of the procedures used. Once you have permanent residence the conditions required for initial residence no longer apply. In order to qualify for permanent residence, however, you need to satisfy those conditions throughout the 5 year period that qualifies you for permanent residence. This means that when you apply to exchange an Initial Residence Certificate for a Permanent Residence Certificate you are still asked to provide evidence as you were when you first got the Initial Residence Certificate. Effectively they are making the judgement that if you satisfy the conditions at the start and the end of the 5 year period then you probably satisfy it throughout.
Obviously whether the Greek law will reflect the rules and whether individual police stations will apply them correctly is always an open question. Personally I will be taking my deeds, my health book and my 22 years worth of tax clearance certificates with me, along with my passport and my Permanent Residence Certificate.