A key European privacy regulator has opened two probes into TikTok’s handling of user data, adding to the popular Chinese app’s regulatory woes on both sides of the Atlantic. Ireland’s Data Protection Commission, which is the European Union’s main regulator for companies like TikTok parent ByteDance that have established their regional headquarters in Ireland, said late Tuesday that it is investigating the app’s processing of children’s data and transfers of user data to China. The watchdog provided few details on the probes but said it first will examine TikTok’s data protection “requirements as they relate to the processing of personal...