Awesome question! While the overall story preserves a third person, omniscient narrator that continuously talks about the ins and outs of Miss Brill, most of what is said comes from Brill's own mindset.This means that the narrator is speaking on behalf of the main character, detailing step by step her daily dynamics the way that Miss Brill would have explained them.
However, those last two paragraphs show a disconnect from Miss Brill's immediate mindset. The last two paragraphs definitely switch points of views. It is as if a sudden event, or situation, suddenly blocks the narrator from the internal flow of thoughts and emotions emanating from Miss Brill. Hence, the narrator goes on to tell Miss Brill's story on behalf of what the narrator sees and knows, coming straight from the point of view of an omniscent storyteller.
On her way home she usually bought a slice of honeycake at the baker's. It was her Sunday treat. [...] She hurried on the almond Sundays and struck the match for the kettle in quite a dashing way.
Notice that the narrator no longer tells the story coming from the consciousness of Miss Brill. Instead, Mansfield tells us a fact that any narrator who knows everything could have similarly told the readers.
But to-day she passed the baker's by. [...] The box that the fur came out of was on the bed. She unclasped the necklet quickly; quickly, without looking, laid it inside. But when she put the lid on she thought she heard something crying.
Again, the narrator can only explain superficially what took place in Miss Brill's small apartment after being shunned by the youths in the park.
Now, in order to re-tell the events through the point of view of Miss Brill, herself, Katherine Mansfield would need to go back into the psyche of Miss Brill and extrapolate very emotion that she may have felt as a result of what happened.
Still, can she do this? If Miss Brill were to acknowledge her emotions instead of saying that she "heard something crying", she would have to accept, at some point, that her life has been wasted building fantasy worlds, and carrying on with menial visits to the park.
It would mean that Miss Brill, as a character, would have to do an entire 180 degree turn, admit her reality, and we are yet to see what would come as a result of that.
Sure, Katherine Mansfield has the freedom to tell the story using whatever point of view she wishes, but she establishes a certain distance from her own character, allowing her to continue her charades and fantasies. Perhaps Mansfield wanted to keep a degree of respect for people who are just like Miss Brill: lonesome individuals who try to make sense of their unfair lives the best way that they know how.
Therefore, the answer to your question is that, if the reveal would have occurred exclusively through Miss Brill's point of view, it would have created an entirely new story; one where she would have to figure out how to stop her current situation and start over as a new person.