It's both of those things at once. There's a lot of humor, there's a love story at the center of it, it has Matt Damon rediscovering himself and seeing the world in a new light, and the way he does that is indeed through being faced with the issues you mentioned.
Also, why is it depressing? I didn't find it depressing at all. There's a group that declares the Earth is 100% screwed in the film and it's framed as a cult and even referred to as one by the main characters. What you're supposed to get out of it is the Earth is indeed screwed, in the long term, if we don't come up with something big, which is something every scientist will tell you and you should already be aware of. Humanity will look for ways to survive. We haven't cracked that nut yet, but the movie is not telling you the nut will never be cracked.
Personally, I didn't find the advertising misleading. The trailer not spoiling 90% of the film is a good thing and what is there is representative of what's in the film, it just goes farther than that, but it's funny throughout, even in the most emotional moments, and the climate change angle is in the trailer.