Does anyone know/recommend books/websites for learning to write business letters in Chinese?
Search 商务写作、商务邮件、商务信函(a formal way to say letter) 、写信的格式 on book.douban.com to find highly rated books in Chinese. Buy them via 京东网、当当网 (=Amazon in China)。(Highly likely that what you find will be books on how to write English business emails, another proof that Chinese companies don't have a strong email culture) Or just see some web posts on this. Search releted keywords on zhihu.com（=Quora）
To my knowledge, Chinese companies don't have a E-mail culture. Middle and small firms usually use Wechat Group、QQ Group (=WhatsApp) to communicate. As long as you write in written language rather than colloquial one, be polite, and remember some appropriate 祝福语 to end the letter (e.g. 顺颂商祺, aka wish your business goes well [formal and literary]), it will be fine.
In China there is not a writing culture as that in western countries (This sentence seems ungrammatical. Who would kindly correct it?). Not so many books or college courses on writing or pubic speech (after all, no election or policy debate in China, why bother learning public speech?). These things are mainly taught in elementary school.