You think too much. Beihai people don't speak Cantonese, but Beihai people speak Beihai dialect, which is just like Cantonese and belongs to "vernacular". It's like Beijingers and Northeasters all speak Mandarin, but there are differences in spoken English. You can't say that Northeasters speak Beijing dialect, nor can you say that Beijingers speak Northeast dialect?

There is no Cantonese training class in Beihai. If you work or live in Beihai, you don't need to speak Cantonese. After a long stay, Beihai people can understand the vernacular or local dialect, and you don't have to learn Beihai dialect, because we Beihai people, Guangxi people or Cantonese people can understand Mandarin. The key is that you can understand Beihai dialect yourself.