Hi Alex. I am not an expert by any means but your very clear explanation of your setup helps me to see that there is nothing you are missing. It’s just the way it is. Ideally if you were plugging into a Mac I think you would have that control… I use a little device called the Qudelix 5K. It is an amazing little unit that can work as a DAC for your iPhone. It is highly configurable and even has one of the best built in EQ setups around. It is a little over a hundred dollars on Amazon and is highly rated. It may give you some of the versatility you are after and even help to key in your favorite EQ. It is also capable of being a Bluetooth receiver so you are not tethered to your device if you are using wired earbuds/headphones. I hope this helps. How are you enjoying your QC overall?
Not an iPhone user, but I would consider looking for a mixer app that will just control the volume of different apps. Googling “iphone audio mixer app” gave me a few results that seemed to do what you need.