There's 2 parts to this:

• Android Auto app (on your phone)
• Android Auto Head Unit software (in your car)

Both of which are currently proprietary,
and would need to be written as FOSS from the ground up by reverse engineering the above 2, which would be a huge undertaking.

Also flashing custom Head Unit software to your car will be very hard, is not well documented, and likely will void your warranty, giving low incentive for developers to even attempt it :/

The best you can do right now is aa4mg (Android Auto 4 MicroG),
which at least allows to replace the proprietary Google Play services with a privacy respecting FOSS alternative and Android Auto's dependencies with empty stub packages:
https://github.com/sn-00-x/aa4mg

Full disclosure,
I helped with writing aa4mg :)

One dreams of a day where it could be a thing. My take is that a drop in replacement is not possible because there is no incentive for car manufacturers to provide that hardware interoperability. They profit too much from the work google does to write the software for them, and all your data they can sell. They want you to buy a whole new car to get the latest features, they are not going to make it any easier on you to extend the lifetime of their product.

There are projects like Crankshaft that allow you to add a head unit to a vehicle that does not have one, but that does not get rid of the android app on your phone. As far as i know all these projects relay on a reverse engineered implementation of the android auto spec: https://github.com/f1xpl/openauto

One could read that implementation and make a client, but i am not aware of one that exists, let alone is actively maintained. Ibl believe the reason is the cost of testing the software for compatibility with all the different auto maker hardware makes this too difficult to sustain. I look forward to other responses to see what others are using.

I remember my uncle just buying a cheap android tablet and flashed some image on it he found on a Russian website. He connected it with a USB cable to the car somehow, he mentioned it's connected to the CAN bus and he could get some information from the car into that tablet.

But what you are asking is a bit different, you want to have the phone ui on the car, for that, it's a bit more difficult.

Theoretically possible but someone would have to reverse engineer the protocol and write a new service that works based on that

There are some projects but all that I’ve seen are open source head units that either: are terrible and aren’t android auto/carplay (eg they only have the most basic of integration, can show notifications and play music via Bluetooth) or they emulate android auto/carplay without the necessary licensing/hardware (so you still ultimately rely on google/apple)

There's probably some form of regulation preventing you to install arbitrary software on your entertainment system, even when you are the manufacturer.