How is this damaged aluminium frame likely to fail?
How is this damaged aluminium frame likely to fail?

Sorry. It's not going to fail, it has failed. It's no longer ridable. The head tube is near vertical making the steering very unstable and the front wheel has been pushed back and will overlap with your toes. The frame tubes are not dented they are buckled and severely weakened. If you ride it the frame will catastrophically fail (either when you hit a bump or brake hard) resulting in a nasty crash.
I hope that if the car driver was a fault you got their details.