Style. The clause "that I...achieve" directly follows the noun "style". That means, with 99% probability that it is an adjective clause that modfies "style". It wouldn't even make sense for it to modify "thoughts". "Thoughts" cannot be "achieved".

"Eloquence" is always about someone's ability to express themselves-- usually in speech, but also sometimes in writing. Someone took the speaker's scrambled thoughts and then interpreted them more eloquently in writing.

I would say that refers to "they," some particular writing in the context where it encapsulates the protagonist's inner thoughts and feelings distinctively. In other words, the whole thing between "just my feelings" and "sophisticated style" is just an apposition for "they." Therefore, the writer could not create such a piece coveted by the readers for which she resonated very much, even though with much envy, especially after publishing her not-so-successful first book.