If you want to be a certified Android system (like all Android manufacturers do), you have to port AOSP to your hardware, install the Play Services as a system app (giving Google root access), install the system apps you want (e.g. Samsung have their own UI, maybe their own camera, their own store that they want to be installed as system apps), pass some conformity tests by Google (Google wants to ensure that it's good enough to be called "Android") and pay a ton of money to Google for the licence.
But as an individual, you can just download the AOSP sources, build them and install them on your phone. It's AOSP, but not Android.
GrapheneOS is based on AOSP. /e/OS is based on LineageOS which is based on AOSP. Those are not Android systems, they are AOSP-based systems. In a way like Linux Mint is based on Ubuntu which is based on Debian. Those are different layers. If you hate Canonical, it doesn't mean that you have to hate Debian, even though Canonical does contribute to software that runs in Debian (like the Linux kernel). The comparison is worth what it's worth, but I hope you get my point :-).
To quote Google's documentation:
> To build an Android-compatible mobile device, follow this three-step process: > 1. Using AOSP, implement Android on your device. > 2. Ensure your device complies with the Android Compatibility Definition Document. The CDD enumerates the software and hardware requirements for an Android-compatible device. > 3. Pass the Compatibility Test Suite (CTS). Use the CTS as an ongoing aid to evaluate compatibility during the development process.
AOSP is how Android is being distributed. Being "Android-compatible" (implementing Android and passing CTS) does not automatically give you access to Google Play, it just unlocks the possibility of licensing it:
> After achieving compatibility, your device is considered Android compatible and you can consider Licensing Google Mobile Services (GMS) and prepare to use the Android trademark.
Google restricts the use of "Android" trademark on hardware, packaging or marketing materials of devices and requires prior approval of any use, but that doesn't make AOSP "not Android". If you insist otherwise, you're going against common use of these terms.
In fact, not just "common use", but even Google's use - AOSP's homepage has this as its headline:
> Android is an open source software stack created for a wide array of devices with different form factors.
It also tells you how to "get the Android source" or "build the Android OS".
Sure, many apps that are being called "Android apps" are in fact apps for the Google Play platform (perhaps that's where you got your confusion from), but that doesn't make Android-based systems non-Android.
Now when someone says "Break free from Android... by installing Android?", either they are having fun by using the two different meanings in the same sentence, or they are confused and genuinely believe that using GrapheneOS does not allow you to break free from the system running on a device that can legally be advertised using the Android trademark.
To that, I answer that GrapheneOS is not a system that can legally be advertised using the Android trademark, but rather a system that is based on what is commonly (and can legally be) called AOSP, which is made of the open source codebase that builds the system that can legally be advertised as Android.
Similarly, in a discussion about kernels, Android is a Linux system, but in a discussion about OSes, Android is not a Linux system. If I write an article about "breaking free from Linux by using Android", where the context makes it exceedingly clear that I'm talking about Linux as an OS and not Linux as a kernel, and you say "it makes no sense, you're talking about breaking free from Linux by installing... Linux", then I think you're confused. As in: you did not understand what the article was talking about.