What software is this update for? iTunes? Mac OS X? Or some obscure OS X driver?

This is the article referenced: https://support.apple.com/en-us/HT208831

I connected my iPhone Mini13 to my Mac running Mojave. I got a mysterious message (from where?) that I have to "update my software." I finally click "learn more" and whew, it's Apple. Apparently it's "software" running on Mojave.

But what happens if I update this software? I don't want to update iTunes - I like it as it is. I really don't want to touch Mojave since I use important 32-bit programs every day—newer OS Xs be for the next Mac I buy and then I'll have two.

So is it "safe" to run this update? In other words, will it have unintended side effects, or will it just allow my phone to connect to Mojave.

In the meantime, Dropbox sees the phone just fine and backs up the photos (which is really what I want to do.)

Thanks to all for being willing provide free technical writing for Apple.