So you can’t switch the low voltage directly with the Inovelli. I would wire a hot and neutral to the line/neutral terminals so that the Inovelli is a scene controller. Then use a smart relay in the place of the old mechanical switch and control it via scenes sent from the Inovelli.
The toughest part will be trying to fit the relay in the switch box. You might need to do it at the fireplace. The relay needs 120VAC to drive it, but you should have that at the fireplace.