I noticed a difference between the Sony X performance and the HTC10 I'm using now if that matters much, not much inside apps but lag changing between music and maps usually - that isn't there on the HTC10. If you can borrow a friends Android (something nice like a pixel or galaxy s8) to rule it out that'd help.
Factory resetting and not relying on hybrid SD Card storage would probably make the world of difference to the responsiveness of Android Auto though.
On paper it's quite a fast phone, so not sure why it's so slow in normal use.
Yeah my mate has an S8 which i'm hoping to test at some point. My phone does need factory resetting i think... it's been awfully slow for a while now, constantly overheats.