Will Vox commander work with smartthings? Either on its own or via HomeAssistant? Do most people use VC and HA sidebyside or do they directly communicate with eachother? There is so many ways to go with all this.
VoxCommando generally can work directly or via an intermediary with a huge variety of hardware and software. How one integrates things with VC is usually a question of one's existing ecosystem, budget, and technical knowledge or interest in reading documentation.
The most common home automation pairing for VC is the Vera because VC has a
Vera plugin that greatly simplifies 2-way interaction.
However, it sounds like you have some things that won't necessarily play well with Vera.
Quite commonly VC users pair the program with
EventGhost -- the program that was actually one of the main inspirations for VC.
I only know of one person who has explicitly mentioned using Home Assistant, but we have a lot of silent users so who knows. Several people use Domoticz, at least one person has posted about how he's using SmartThings.
In each of these scenarios there's probably more than one way to integrate the home automation controller with VC. In some cases it's possible the additional intermediary software or hardware would be redundant if the user had a better understanding of how http requests work or TCP or Python scripting or whatnot.