How to install iOS 14 on an iPhone 6?

I think the main difference between the iPhone 6 and iPhone 6s that stops iOS 14 supporting the iPhone 6 is probably the fact that the iPhone 6 has 1GB of system RAM (not storage), and the iPhone 6s has 2GB of system RAM.

There is not a lot that could be done to make an OS designed to run in at least 2GB of RAM, work on a system with only 1GB of RAM.

Even if you were able to persuade iOS 14 to install on an iPhone 6, it would run like a dog, if it would run at all.

iPhone 6 does not support running any version of iOS beyond iOS 12.5.1. So it's not possible to install iOS 14 on it.

Apple routinely drops supports for older devices when releasing a new version of iOS. But also, there are some years when Apple does not drop support for any older device. E.g. All the iOS devices that supported running iOS 13 can also run iOS 14.

Now to answer your specific questions:

Does the App Store just identify my phone as iPhone 6 via a physical identifier in the phone, and that prevents me from downloading any iOS version beyond 12.5.1?

Yes. There is a physical identifier associated with every iOS device generally referred to as A model number. Depending on the variant the A model number for iPhone 6 could be any of A1549, A1586 or A1589.

How might I get around this?

There is no official way to get around this. iOS 12.5.1 is the highest version of iOS that you can install and run on an iPhone 6.

You need at least an iPhone 6s or later to run iOS 14.