The photographs of Crown Prince Vajiralongkorn published in German newspaper Bild are genuine. They have not been doctored or faked.
The photographs are likely to be at least a few days old. Vajiralongkorn was in Thailand today and yesterday. But the images are real.
However, as several people have pointed out, Vajiralongkorn did not have tattooed arms at the Bike for Dad event, nor was he tattooed when photographed in a swimming pool in Germany with his son Dipangkorn last year.
It's possible that the tattoos were newly done, and so it was painful to wear a shirt, and then that he felt cold so borrowed one of Nui's singlets. It is also possible that the tattoos are not real, in other words that they are temporary and have been painted onto his skin but not tattooed into his skin. This still leaves the question of — why?