I'm not sure that what you see as sold out is a predictor of anything.
The number of foot pilgrims has steadily increased by a few percentages year after year. Especially Galicia was prepared to receive a whopping number of 500,000 pilgrims this year - up from 350,000 pilgrims in 2019 (pre-Covid). I doubt that this number will be reached in 2022, even if there is bit of a surge due to cancelled trips in '20 and '21.
Besides, a large number of Camino pilgrims is made up by Spanish pilgrims, and they did walk in '21. Over 130,000 pilgrims so far this year who didn't cancel their trip.
The Caminos, especially the popular ones like the Frances and Portugues, will be busy next year because that's the way it is - Camino walking is becoming more and more widely known and becoming more and more popular. And May is a popular and busy month for international pilgrims anyway. If the restrictions on municipal and other albergues is lifted by May 2022, ie if or when they can use their full accommodation capacity again, then 2022 will be just that: yet another busy Camino year. At least that's my prediction. And my advice would be the same as always: book the first few nights, especially if you start with the section SJPP-Pamplona, and then either book ahead for the next day or for a few days if you want private rooms, or don't book at all if you are happy with shared dormitory accommodation.