What happens if there is no menu when I connect my iPhone to the mac computer?

Thanks... as below.

Note - I was not wanting to sync the Mac with my phone. After connecting the cable, on my phone screen a message popped up and asked if I Trust this computer, and I gave my code to give the phone access. When I press the Trust button shown in the screenshot, it goes into a an endless waiting loop, which is what I expect as there far too much on my main computer to synchronize it all onto my phone! I don't want this to happen, and cannot wait endlessly, so quit Finder to get out of the loop.

Thanks!

My phone is connected by a cable, and I can see my phone as in your screenshot, but not any menu underneath.

I should mention that my phone is iPhone 7 with system 14.6.

Although almost nothing is stored on the phone, but storage information claims the phone is full. It is no longer able to show a breakdown of what is causing it to be full, but it was never the photos etc, only anonymous grey storage.

In my attempt to give space for the apps to work, there is almost nothing in my iCloud account as I moved all my photos into external hard drives. I have only a small number of apps that are active, after offloading data, so I would expect to have about 20 Gb of free storage but have only about 500 Mb out of 32 Mb. I can no longer update apps, or update the system using iTunes.

My hope is that by updating the system from my Mac, I can recover functionality of the phone.

Thanks again.

Just to conclude. The update succeeded, and now my old iPhone 7 displays a sensible amount of free storage, responds quickly to streaming services, and allows me to update the few essential apps that I often use. The new software version that was provided by the Apple site was OS v. 15.7.6

I suppose at some point I will really need to buy a new phone etc., but I would be happy be to get at least another year of good use from this model. I paid about 70,000 yen or 600 USD for an unlocked phone and would like to get at least 6-7 years usage, given the price.

OK... I tried again, and now I see the menu.

Thanks, Peter