There isn’t a good way to move a whole lot of photos from an iPhone directly to an external storage device attached to the iPhone.
If you don’t already have one, get a backup of the iPhone contents:
How to back up your iPhone, iPad, and iPod touch with your Mac - Apple Support
If you want to store your photos locally on macOS and not iCloud, shut off iCloud Photos and download all photos locally, and then import the contents of the iPhone into the macOS Photos app library:
Overview of importing photos and videos into Photos on Mac - Apple Support
I keep photos locally on macOS, as the network around here has been unstable and slow up until fairly recently. And I have over thirteen thousand photos and videos; a lot of data. (This local storage does require me to use cable sync to transfer files to the macOS Photos app library, and sync those back to the iPhone.) iCloud Photos does work, but that can take a while to sync a whole lot of data, and the network needs to be stable.
By “most up to date software”, you’re running iOS 16.6, and macOS 13.5?