Android is NOT Linux.

It very much is, by the most basic technical definition of being an operating system based on the operating system kernel called Linux. I am sorry if this upsets Linux fans but this fact is easily verifiable.

Note that when I say Linux I mean only the kernel, i.e. the thing actually called Linux, and not any of the assortment of operating systems built around it (this includes Android) or any Linux-adjacent projects like GNU, systemd, GNOME, wayland, etc. Any operating system that includes those is a Linux operating system if it's built on the kernel called Linux, but only the kernel is a prerequisite for being "Linux."

Regardless it's not an answer to the problem posed by the OP, which is that "Play Store blocks Aurora Store." Anyone using Aurora Store is doing so because they require an app from Google Play Store. Whether they are using a "Linux phone" or not is irrelevant at this point because if they are, they are probably using an Android environment to run proprietary Android apps that come from Google Play Store and require Google Play Services.

This is why I say "Linux phones" are for the most part a red herring in the mobile software freedom discussion. A "Linux phone with Waydroid" is just an Android phone with extra steps. It's not like Wine/Proton which isn't Windows but an entirely independent implementation of Windows API. It's literally just running Android in a container. They would be nice to have at the final step of the freedom ladder after you've already removed yourself from the google ecosystem, but they are not the first step on the ladder.