I was doing
Camino Frances last year in July/August.
From Pyrenees to Astorga you can walk freely without making any bookings. Even if you arrive a bit later. From Astorga onwards the pilgrims numbers did pick up significantly. Sarria pilgrims tended to stay in the main stops and for them booking places ahead was an issue. There were no issues in finding a place to stay between the traditional spots.
I did hear that on the Norte the bed race was an issue. Number of albergues went down with Covid, but popularity of the trail seems to have recovered.
When I walked Portuguese from Lisbon to Porto and then along the coastline in May (pre-Covid), I never needed to book in advance.