Given such an essential service, I personally don't think it's important they are turning a profit. But is it run efficiently? I have no idea and this article doesn't really go into it. Had a quick search and found Australia Post's Efficiency of Delivering Reserved Letter Services. Haven't read it in full yet but first glance looks interesting.

And from some quick digging, I found that every year their revenue increases:

2022 $8864M
2021 $8208M
2020 $7499M
2019 $6990M
2018 $6877M

From their annual reports page: https://auspost.com.au/about-us/news-media/publications#annual