Yes I store all of my e-bikes in the house including a bunch of batteries. Good quality, well made, well regulated batteries are fine to keep indoors and it is where you should keep them. I have one Bosch equipped bike, one Brose equipped Specialized and one SL Specialized. I have no real worries about them, they are all UL listed and well built. I don't keep the charger on top of anything flammable and try not to store any flammable liquids near them and make sure they are being charged properly with no metal in between the rosenberger plug on the Brose bike.

The e-bike battery fires are usually unregulated batteries on cheap bikes and a lot of times the fires are caused by someone charging way way way too many unregulated batteries with similar chargers.