You'll be fine Colin, I departed BER last week using printouts of all the documents, no phone. Ryanair double checked everything, once in the check in queue and again at the gate.
They're adamant that all paperwork has to be in English, especially the negative test, or they'll refuse boarding as 'it won't be accepted in the UK'.
A couple of people were asked for email proof that they'd ordered a Day 2 test! It didn't happen to me, but I would just have argued that I'd entered the order code on my passenger locator form as required.
I used the eGate on arrival and that was that, no further checks at Stansted.
I'm now doing the online Einreiseanmeldung which can only be done 2 days before returning to Germany. It generates a PDF that I will need to print out, and in the PDF is a link for uploading proof of vaccination. Two steps in this process require pin codes, which they'll send either to an email address or a phone number. Hope this helps!
