No, it does not have any more access than any other app, as it work on unrooted devices too.

That said, it has to be compiled for older Android SDK level because newer levels prevent apps to run executables they downloaded on their own and not bundle with the APK, even isolated. Android may disable compatibility with the older SDK some day but for now it works.

sorry, it was my understanding that Android apps have lower level access to the Android OS than iOS apps allow, that essentially iOS apps are sandboxed? And that this was what was allowing Termux to do everything it did in Android.