Is there a way to expose the button “actions” like single press, double press etc, to HomeKit appropriately? It seems that HomeKit itself has support for button actions, but the HomeKit integration does map the actions.
My workaround now is to let the button flip a switch that is exposed to homekit, and then have an automation that flips the switch back after 2s. And in the Home app, you trigger on the switch being turned on.
If I remember correctly you need to go into your profile (in the side bar menu) and enable advanced mode.
For some reason this enables an extra step within the HomeKit Bridge Integration, so when you configure one there ends up being a third step where you can choose to expose buttons.
It’s a bit annoying because multi press buttons end being separate buttons and you have to blindly assign something to each one to figure out which button is which press combination. Which took me AGES when I tried my first switch which had I think like 25 possible combinations 
The only reason I needed this was because I hadn’t moved all my Apple Home devices into HA yet. So this definitely gave me the kick in the butt to hurry that process up so I could just move all the automations into HA where the buttons were labelled properly.