There's no "the" HN app - only a bunch of different third-party projects. If one isn't working, there are plenty of others out there to try.

Apart from broken links, what is the benefit of using an app other than the web browser to peruse HN on mobile?

They work in the one I use: “Octal” for iOS

Works in MiniHack on iOS (unofficial)

works on Materialistic for Android