This website lists most of the tourist sites in Santiago along with operating hours.
Web oficial de turismo de Santiago de Compostela: etapa final del Camino de Santiago
de Compostela. Ofrece información sobre Hoteles en Santiago de Compostela y la Catedral de Santiago.
I was surprised to see that the Cathedral museum (along with other cathedral sites, like the Pórtico de la Gloria) is closed on Sunday afternoons and Mondays. That is standard across Spain, but lots of the most popular tourist sites, like the Prado Museum in Madrid and the Alhambra in Granada, are open daily.
I think it’s generally a good idea (if you are planning to visit museums, etc in any city along the way) to try to avoid arriving on a Sunday. You will typically arrive just as everything is closing, and then will have to wait to Tuesday to see the sites. But there’s plenty to see and enjoy in Santiago even when all the tourist sites are closed!