Why might Itunes for WIndows not recognize that my iPhone has been updated to the latest iOS?

JoshuaCM wrote:

My version does not have an option under help to check for updates.

Are you sure? It's on the Help menu, but above the About iTunes line:

I'm led to believe that the version from the Microsoft Store doesn't have the update option because it updates automatically, meaning that there is no need to turn it on or off. But in addition, my understanding is that it also doesn't show which version is installed, because it is fully automatic.

JoshuaCM wrote:

The itunes version is12.12.10.1

Where did you find that information, because as stated the Microsoft version doesn't tell you which version it is? Even if it did, it updates automatically so it is difficult to see how your installed version could be two updates behind the current one.

There is something under preferences to automatically check for updated software.

Again, that suggests that you have the Apple version of iTunes, in which case there should be a Check for Updates option on the Help menu. Even if you had the Check for new software updates automatically option turned off there would still be an option to check manually.

The first thing to do is update your iTunes to the latest version, which is 12.13.1.3 You do not need to uninstall iTunes; instead you can click on iTunes' top bar menu Help/Check for Updates and it will guide you through the procedure.

Since the version of iTunes that you are using was released there have been two updates.

I'm at a loss to explain this then. I have to assume that your copy of iTunes came from the Microsoft Store, in which case, as stated, it should update automatically and not provide an option to avoid updating. All I can suggest now is that you check to ensure that your iTunes can get online. Make sure that your anti-virus is not preventing access.