During the 1890s, while at the same time a student, Willa Cather

The original sentence has some problems:
-Use of "while" + "at the same time" is redundant.
-Use of past perfect "had written is not required since there is no sequence of events.

Pre-thinking:
In this question while is used to denote same-time events, so correct answer choice would be:
While Willa Carther was a student in the early 1890s, she wrote theatric and music reviews....

Whit my pre-thinking I tried to find an answer, and B was the best fit. However, the structure of this option is the following:
While + Noun modifier, + Clause:
While a student in the early 1890s, Willa Cather wrote theater and music reviews that were often uncompromising in their criticisms.

I know that the uses of while are the following:
1) Show that two events are happening at the same time: Ex. The phone rang while I was writing this post.
2) Denote a contrast. (although)

But when used for same-time events, Can we use "while" before a noun modifier or we need While + Clause1, clause2 as stated in my pre-thinking?
I got the right answer choice B, but just wanted to validate this grammar query.