Why does this pop-up not say what software is being updated?

The popup from the support document you posted from only refers to firmware updates for iTunes / Finder to connect to the iPhone.

It does not have anything to do with updates to your main macOs version or other software on your Mac. It's strictly for the connection to the iPhone only. Nothing else.

As explained on the above link…

"When you connect your iPhone, iPad, or iPod touch to a Mac with macOS 10.11 or later, you might need to update the software on your Mac in order for it to recognize your iOS device.

If you see "Software update is required to connect to your iOS device" on your iPhone, iPad, or iPod touch

As the computer is listed as running MacBook Pro 13″, macOS 12.2. there could be several updates to be installed including the Current stable Monterey 12.6 plus Safari 16.

This is a bit of a " Roll of the Dice " at this juncture in time without more meaningful information provided

P. Phillips wrote:

As the computer is listed as running MacBook Pro 13″, macOS 12.2. there could be several updates to be installed including the Current stable Monterey 12.6 plus Safari 16.

FWIW, there is no "pop-up" message for Monterey updates. The pop-up was caused by connecting the iPhone.

Why don’t you show us which pop-up you are talking about? Otherwise how can anyone help?

Indeed.

Valid point 👍

Thought the extraneous extra information maybe be useful to the OP too.