I am answering, as I’m leaving for the Camino Mozarabe on Sept. 2nd from Vancouver, going to Almeria. You don’t have to isolate. You should bring a proof of your 2 vaccines and fill up that info. https://www.spth.gob.es/. Whenever you go, have a great Camino.
As noted above I applied for and received the French Pass Sanitaire which I was required to show on arrival at CDG and when checking in to the Albergues in St Jean and Orrisson. I am now in Roncesvalles and they did not ask for any data. I did not have to isolate because of the health pass.
I have run into some small issues with Albergues that are closed when i had expected them to be open. I did not book ahead for Uterga but no problem as I arrived around 13:30. I hoped for the same in Lorca but both Albergues are closed, as well in Villatuerta.. An extra 9.9 km at the end of a warm day to Estrella. I have booked for tomorrow. I will comment further as I go.
I am now in Rabanal del Camino and I am booking ahead due to so many Albergues being closed. In Rabanal at least 50% ate closed. I am trying to book 3 days ahead. It's not as enjoyable as my 2 previous Caminos