I have the same problems with my 2019 Impreza. It responds sooner if I'm not in reverse, but I am usually in reverse first because I need to back out of my garage. It usually doesn't respond to the volume knob messages until a second after shifting into forward. I say "messages" because the turns of the knob appear to be queued up somewhere, but it doesn't have as much time to process those while it's displaying the rear-view camera on the screen.
I have a problem like this in my 2018 Dodge! The bluetooth takes a wildly variable amount of time to connect when starting the car, and the bluetooth doesn't have an input gain option, like aux input does.
This means I need to turn the volume up a ways to hear anything over bluetooth. This also means that between starting the car and bluetooth connecting I'm getting blasted by some random radio station at increased volume.
It's still an issue in the 2018 Impreza. I've gotten used to it now, but it's still frustrating. Especially if I ended the drive with a phone call. On phone calls I have to really crank up the volume (nearly max) whereas for music and other things I have it very low (10-15? The numbers mean nothing to me, not loud). So when I turn it on after a call I get blasted by NPR for about 5-10 seconds before the audio volume dial actually responds (sometimes it takes the early attempted dialing down but delayed, other times I have to try and dial it down again).
Other than audio controls, though, everything else is responsive, I don't notice any lag. It really seems to be an issue with their stereo system. Either it's not fully booted (and can't respond to controls yet) or there's some mediating system that transmits the controls which isn't booted up as quickly.