Sort of a rehash of this WTH from 2020. As it now stands the iOS companion app can work with multiple HA instances and you can easily switch between them, I know this because my wife does this on her phone!
I, however, am not beholden to the Apple and have cast my hardware vote with Android devices. The companion app, which I use all the time, does not have the ability to switch easily between HA instances. As I currently manage several (because of vacation rentals) this is a major pain point for me as I have to either log out of my home HA and into my target one, or I keep a browser tab open on my phone to the target instances (which is my current method).