a software update is required to restore your iphone

I see this too, and have for a couple months. The only difference is that my phone doesn't get bricked, and I have no actual problem doing things over the tethered connection, so the warning appears to be bogus.

The Apple KB article says, "You might see this message if the software on your Mac needs to be updated to support the newer software on your iPhone or iPad." So it sounds as if the new software is destined to be installed on the Mac, not the iPhone, but is still failing.

The sequence of operations I always see are:

Plug the USB cable between the phone and the Mac. Immediately see this:

Click Install. Get this box:

At the same time, my iPhone asks me if I want to "trust this computer," and I tap in my open code.

Then I get:

...quickly followed by...

I'm running the latest update of Monterey, so there should be no reason that I should need to update my software for this to work. (It also failed before Ventura was released, so at that time it was Apple's newest software.) My phone is an 8+.

Restart your Mac in Safe mode→Start up your Mac in safe mode - Apple Support, then repeat the sequence you posted. There is something blocking the installation. If you have any 3rd party “helper” or antivirus apps on your Mac that might be the cause.

No joy.

I had a devil of a time getting into Safe Mode, trying both the laptop's own KB and then a USB KB. When it wouldn't even respond to the PRAM zap sequence, I recalled I had established a FW password (to allow the unit to boot from an external some time past), so I disabled that. Then I was able to boot into Safe Mode.

But apparently Safe Mode also disables the mechanism that mounts the iPhone to your finder sidebar, because it didn't show up and I didn't get any of the dialog boxes. I established that the tether cable still functioned fine by importing some photos over it, but none of the "higher functions" were enabled in Safe Mode.

So I rebooted into normal mode to see if the absence of the FW password would solve the "can't install software" problem. But it still failed. So Safe Mode isn't a useful diagnostic or amelioration.

FTR, I don't run any AV or anything else that would obviously hinder this function.

What is the error message when it fails? If it is a Mac have you tried restarting the phone in Safe mode→How to use safe mode on your Mac - Apple Support

You have to click Install. That will update the iOS communications driver on your computer.