As a precaution I took a PCR test two days before I left. Negative result emailed to me and printed out.
Proof of vaccination also emailed to me through NHS and printed out.
The Greek passenger locator form also done by email and printed.
Return procedure documents in similar fashion.
I avoided all use of a "smart" phone during my travels as there can be logging in to wifi hiccups. Print it all out and you will feel far more relaxed. Good luck.