My husband and I have walked both the Camino Francés and the Camino Primitivo as vegans, and we had no problem finding food along the way. There are quite a few albergues that serve exclusively vegetarian/vegan food, and many more that will provide a vegan option on request.
I can only think of one albergue that was not able to provide a vegan meal when we requested it. Vegan meals are available at the following albergues (I have eaten at many of these myself, and others have been recommended by other vegan pilgrims):
La Vita è Bella in St Jean Pied de Port
Albergue Maribel in Cizur Menor
La Perla Negra in Azqueta
Parochial hostel in San Juan de Ortega
Albergue San Bruno in Moratinos
Cuatro Cantones in Belorado
Orion in Castrojeriz
San Antonio de Padua in Villar de Mazarife
Albergue Verde in Hospital de Orbigo
Casa Las Aguedas in Murias de Rechivaldo
Monte Irago in Foncebadón
El Trasgu de Foncebadón
Albergue de Ada in Reliegos
Alea in Ponferrada
El Serbal y La Luna in Pieros
Miriam Las Herrerías in Las Herrerías
El Refugio in La Faba
El Beso in A Balsa
Molino de Marzán at A Leda
Casa Domingo in Ponte Campana
Ultreia in Arzúa
I brought my own food to Roncesvalles and self-catered, so I'm not sure what the meal options are there. I do know that there are vending machines at the albergue that sell microwaveable food, and I was able to supplement my provisions with a pisto (a Spanish dish similar to ratatouille) from the machine. I believe there were one or two other vegan options too.
If you speak some Spanish and learn a bit about Spanish cuisine and which common dishes are already vegan or can easily be adapted, it will make your journey much smoother.
Do have a look at my article "6 Tips for Eating Vegan on the
Camino de Santiago", linked in my signature below.