Depends somewhat. Home Assistant has its own app that works pretty well. Generally other apps don't integrate with Home Assistant, but rather the other way around with Home Assistant having a plug-in to allow it to control and interact with other hardware/software. Everything is controlled/managed by Home Assistant so when you need to issue commands or setup triggers its your one stop shop.
I know there are voice control plugins for Home Assistant that are reviewed reasonably well, but I don't personally use them so I can't say what models of mic work well or not. My usage is pretty minimal with simple timers and/or things like presence and temperature sensors being sufficient to meet all my automation needs supplemented by the occasional custom UI button on my Home Assistant dashboard accessible through the app or web interface. Personally the rule I try to follow for all my IoT devices is to avoid Wifi if at all possible in favor of standard mesh network tech like Zigbee or Z-Wave that way it's literally impossible for my "smart devices" to call out to the Internet without me manually installing some kind of bridging software in Home Assistant.