Pop-up window saying "Enter your password to Install Software Update" on my iMac

There is nothing incorrect in being old-fashioned as long as you know where this Software Update is being presented and from Whom

Usually, in Ventura Setting / Preferences >> Software Update would / could have a Red Badge appearing

Meaning the Computer has communicated with the Apple Servers and yes an upGrade is available

I would be highly suspicious IF the computer Did Not Qualify for any upGrades

But as mentioned it is exactly the opposite - right

As for Fake Induced by Malware

Malware / Adware just does not get installed on the Computer

It would required you the user to give this Stuff to install by Entering your Computer Password and then bypass the builtin protects with the Operating System

Mac app security enhancements are sufficient to protect computers from malware.

Another good User Tip from a colleague of mine re-malware

Source: User tip from @Kurt Lang

What is malware? - Apple Community

Likely not malware, and yes, you do need to confirm the operating system installation with your admin password.

I have never enabled automatic operating system updates in decades of using the operating system. I do allow it to automatically install security responses and system files, but everything else is purely manual. That way, I get a 1:1 correlation between deliberately clicking the Software Update button and that password request dialog. Additionally, I get to install the operating system when it is convenient for me.

OP wrote " I'm running macOS Ventura 13.6.7 on a 2022 M2 MacBook Air, and the "Automatic updates" setting is on. "

This specific computer Qualifies to run macOS 14 Sonoma as well as macOS 15.3.1 the Latest version of Sequoia

macOS Sequoia compatible Computers 

macOS Sonoma is compatible with these computers

If you are that obsessed about upGrading and feel the Software Update Applet is not for you

You can take direct action that is totally under your control

In the Terminal application copy and paste the below command followed by the Return key

softwareupdate --list-full-installers

It will Only Search for all available Full Installers for versions of macOS this computer Qualifies to run

The question is now, do you trust what Apple is offering as an upGrade ?

If Yes, proceed to upGrade the computer

Always make a Time Machine Backup  before doing any upDates / upGrades 

An aside

Not getting notifications of you previously posting which worth reading I must say