Okay...

Theme: Historical Chinese/Korean/Taiwan/East Asian

FL is spoilt/comes from a rich family and then one day her parents send her to get trained by a 'master' 

Master can be the best in martial arts/kung fu/meditation/fighting et cetera wise 

She then has to overcome challeneges, getting accepted by the master, giving up her belonigng and life luxuries to take on being a discipline or student for the 'master'

There should be setbacks/progress/character improvement

BONUS: Romance elements

 Buried City to Shut All Lights? I don't know that FL would be considered rich but she's very innocent/sheltered/spoiled and sent to become the disciple of the ML. Over the course of the drama she undergoes a tremendous amount of loss, tragedy, and character growth. There's a sequel movie that wraps up the open ending of the drama with a happy ending but I felt it somewhat undid the FL's growth.

I'm not sure if this fits, but I believe One and Only [2021] somewhat follows that theme. [It's a prequel show]. The original book was split into two parts, as is the show.

One and Only follows a MC who somewhat fits your description but she also doesn't. She doesn't fall into the 'spoiled' category but she was definitely sheltered and she undergoes a lot of character growth in this show. She starts off as a 'selectively' mute [likely from trauma if I remember], shy and timid young girl but blossoms throughout the show.

There's romance, character growth, setbacks, progress, master and disciple as well as other disciple relationships. I really can't say much without spoiling but...

It's a SE. It might turn you away, which is understandable - but the sad ending matches very well for the love story. It also plays into the sequel, which is a reincarnation HE. 


Also, have you watched Eternal Love?