Thanks so much for these instructions.
I'm running MacOS El Capitan 10.11.6, with iTunes 12.8.2.3 installed, and I was having trouble connecting my iPhone 7 running OS 14.1. The fix for me was slightly different - I just had to download and reinstall iTunes while my iPhone was connected to my Macbook!
As soon as the 'Install iTunes.pkg' had run an iPhone 'Software Update' window appeared on my Mac, which then installed in a few minutes. When I then opened iTunes the iPhone appeared connected as normal (and I did not lose any iTunes data due to the reinstall)!
The difference to your scenario:
When plugging my iPhone into the Macbook the iPhone would charge, and the Macbook Photos app automatically opened and recognised the iPhone, prompting me to sync the pictures from the phone, but I couldn't get that iPhone 'Software Update' window to show on the Macbook, even when I opened iTunes - while the phone completely failed to appear in iTunes.
I opened the 'iTunes' Unix executable from /Applications/iTunes.app/Contents/MacOS/ in Terminal, and it stated the following error:
BootedOS device needs updated MobileDevice.framework; ignoring device
ATHostConnectionDestroy 0x7f80362119b0
This site provided the reinstall fix suggestion after similar issues were reported with IOS12 and High Sierra compatability.
Thanks again