Sorry, forgot to add the other thing.
Go to the hospital or vaccine site and show your booklet and ask them to please put something on paper with at least one official signature and a stamp from the vaccination site or hospital confirming that you had the doses … and make sure the paper is dated, has your full name on it , along with your passport number and No de Expediente for your precaria. I also did this. I haven’t needed to use it, but as I am waiting for my DNI to arrive, I have this as a backup to my vaccination booklet …