Your quoted sentence doesn't make sense.
If you write
- He became very frustrated that his boss appraised him wrongly and it affected his career.
It would make sense, and it would mean "Because of his boss's wrong appraisal his career is being affected. And that's why he is frustrated."
So...that is a set expression.
- He became so frustrated that he started to look for a new job.
Now consider sentence 1 and sentence 2. While sentence 1 states the reason of your frustration, sentence 2 states what you did because of it.
Places where so can be replaced by very
- He is so/very angry about the way the event unfolded.
Your sentence -
She became so frustrated with the lack of feedback from her boss that she decided to look for another job.
What is the cause of her frustration - The lack of feedback from her boss.
And effect - She decided to look for another job.