software update does not load

Is the example image in this Apple article what you see?:

If your Mac says that a software update is required to connect to iPhone or iPad - Apple Support

If so, Grants instructional correct. It usually only appears if you are running macOS 10.14 Mojave or older and are managing your iOS device with iTunes. The article fails to make clear how the update works.

The small, quick download is a patch for iTunes only to make it compatible with newer iOS version. It will NOT change your macOS version. I've applied it several times to two pre-Catalina Macs with zero susses or changes to my macOS versions.

For Catalina 10.15 and later, iOS devices are managed through the Finder, appearing in the Finder sidebar in the was way external drives appear.

Restart your Mac and try again.

If this happens only when you connect your iPhone, you need to accept that update at that moment, as it will not appear separately.