How to write and structure a modern professional follow-up email like a native Chinese speaker?
主题：YYY分部ABC职位申请之跟进


  尊敬的XXX，   
  
  您好！
  
  望您安度时艰，身体无恙！
  
  此函意在跟进本人近日申请伦敦分部职位一事。本人已经由ZZZ渠道递交对ABC职位之申请，以担忧贵方尚未收到之故，随函再附本人履历及求职信。效力于贵司之心愿迫切，所以确认再三，还望海涵！
  
  如有疑问，请与本人联系。感谢拨冗垂阅，敬盼回音！
  
  此致，
  
  祝好！
  
  署名


I don't think it is just about one or two phrase substitutes, but the cultural differences behind writings... We tend to use more literary and concise expressions in mail, and we have a system of 敬语/谦词/雅言...

e.g.

安(safely)度(go through)时(recent/present)艰(tough situations)

无恙(without any illness)

此函(this letter)

意在(aiming at)

跟进...一事(follow up the thing that)

经由(via)

渠道(channel/means)

递交(submit)

以...之故(for the reason that…)

海涵(forgive me for [anything, here it means that I impatiently send another letter to check for my application (In Chinese culture, ask repeatedly for the same thing is rude)])

拨冗(kindly spend the time [for my business])

垂阅(read [my letter])

敬盼(sincerely look forward to)

回音(reply)

These expressions I list are "advanced" forms of what we would use in oral language, which we are supposed to use in a proper letter.

And


I'm very keen on joining YYY and I'm more than happy to discuss how I can be an asset to the team.


seems irrelevent in a follow-up letter (at least in Chinese cultural), so I rephrase it and append it to the previous paragraph, making it a cause explaining why I follow up the application business.