When I was playing with a Dualshock4 controller, I found the game works surprisingly well with the help of steam controller input, and in-game icons can actually be configured to yours. One thing I noticed however, despite of having a controller support, Angel at Dusk doesn't seem to register the angular input from my stick. Ship is only able to move around in either full speed, or full stop, even I was just pushing my stick very slightly. It makes the speedy crafts difficult to dodge bullets. Idk if it's a intended design choice because the genre seems in favor of keyboard-control or otherwise the D-pad. Thankfully we got the steam input that can partially fix this. Here's the instructions

First of all, you need a compatible controller with steam input and I'm sure 90% percent of them will work.
Then after connecting your controller with your PC or Laptop, you should be able to see this steam input button enabled in your interface,



and you'll be able to configure the input by clicking this bar:



Next, go to the "Joysticks", change the left stick to "Directional Pad", and configure the four directions of movement to their corresponding ones.


Then, hit this icon to setup the stick to Analog Emulation


The parameters don't have to be exactly the same as mine. You can try a different set that fits your hands.
Now you should be able to utilize the analog input by your stick and move very precisely :)

(you would probably have to use the D-pad to browse the in-game menu since it's janky with an analog stick