A popular fan-made theory claims that Baizhu and Pantalone could actually be the same person and his main job is to gather as much information as possible from Liyue.

Source: https://gamerant.com/genshin-impact-concept-pantalone-archon/

's ongoing Lantern Rite has seen players return to Liyue for the annual festival with a variety of quests and events to enjoy.

Source: https://gamerant.com/genshin-impact-hu-tao-lantern-rite-trailer-detail/

Story-wise, there is not a lot of information about Baizhu other than that he's the proud owner of the Bubu Pharmacy located in Liyue Harbor.

Source: https://gamerant.com/genshin-impact-leak-five-star-weapon-jadefalls-splendor/