The Leon section is definitely a project that is early in development so there is limited info. There is apparently some route markings done - there is a pilgrim welcome in Quintanilla, and also accomodation in hostals in Bembimbre. At Branuelas - some have arranged pick up by accomodation (i think it was the campsite at Villamejil) or take the train back & forward overnight to Ponferrada or Astorga.
Andre is right there are several wikiloc maps available - these guys walked in 2023 and also took photos for instances
Cogorderos - Brañuelas…Vía Kunig. Hiking trail in Cogorderos, Castilla y León (España). Download its GPS track and follow the itinerary on a map. Cogorderos - Brañuelas
www.wikiloc.com
There are 2 options to start - either Villadangos which follows on track beside road to Celadilla and then parallel tracks through fields to Santa Marina or from San Martin which follows the canal to Santa Marina del Rey.
There is further info on background at
A finales del siglo XV, Hermann Künig, perteneciente a la orden de los Siervos de María tenía en Vach, decidió peregrinar a España: El camino de Künig.
www.elcaminodekunig.com
There is also a Via Kunig Facebook group - at least 2 folks have walked recently the Leon section.
But as for the viakunig.eu the information is developing - a few weeks ago there was no Leon section, and the section 3 to Villamejil is less a week old - so I would think it more may appear quickly enough.