Why do you think your Norco would get "destroyed" riding it off-road? You've already got an upright-riding bike with disc brakes, flat bars, and clearance for wide tires. That sounds like a good base for off-road riding.
There are three things that influence your speed: wind resistance, rolling resistance, and (following in a distant third) weight.
If you want two bikes, then it would be worth considering one with upright bars (like a mountain bike) and one with drop bars. That would be what might make a difference with wind resistance. As it is, though, your hybrid and whatever mountain bike you might get would have pretty much the same bike position, and pretty much the same wind resistance.
Rolling resistance, of course, depends on your tires. Supple tires with fewer knobs roll faster than tires that have a stiff sidewall and/or knobs. Supple tires, such as those offered by Compass, are expensive, but in my experience, they ride great. I also have had very few flats with Compass tires.
So, in your current situation, and depending on how big a tire your current frame fits, you might either get the big slick Compass, 55mm wide:
https://www.compasscycle.com/shop/components/tires/700c/compass-700c-x-55-antelope-hill-tc/ or the cyclo-cross-ish knobby 38mm wide tire:
https://www.compasscycle.com/shop/components/tires/700c/compass-700c-x-38-steilacoom/Which might work best off-road would depend on what your trails are like. The fatter slick would be good on sand (and bare rock- probably not what you've got!), and the knobby would be better on vegetation and mud. Either one of them would also probably be quite a bit faster on the road that what you've got on your Norco AND they'd be at least competent off-road if they're good for your trails. The only serious contra-indication would be a lot of sharp rocky terrain, which poses a danger to the sidewalls. Now, ideally, of course, you'd go with still fatter tires. I run 700c x 2.3" on my mountain bike, and nowadays, of course, you can even go much fatter. But that would likely require a second set of wheels. Sure, you could just change tires- but that a pain enough that you'd probably never do it.
Mountain biking without suspension is totally possible. In fact, it makes you a better rider. And the better tires (even though fatter) will likely make your road commute easier.