In late September, I was in Jaca and asked the Turismo staff if the trail to San Juan de la Peña had been improved or maintained, and a staff member (who was in a local hiking group) said that it had not been. However, he told me, the signing had improved, and it was marked as a trail of medium difficulty, and he would not advise pilgrims to use it.
A few days later, as I was sitting in the hot springs at Tiermas (km 336 south of the road between Berdún and Yesa, on the north shore of the Embalse de Yesa) to recuperate from that particular path, much of which is walked alongside a busy carretera, I spoke with a woman soldier from the Principe de Asturias regiment, who was training at the Mountain Military School in Jaca. She told me that she and a few of her comrades had done it as a training walk when they first go there, and she said it is not to be recommended for day-hikers or pilgrims. And unlike Tiermas, she continued, there were no mud baths at San Juan de la Peña.