I agree that the anime has a tone problem.
However, rewatching recent episodes, it honestly feels like the most out-of-tone section is the intro and outro (there's a few other sections, like the elevator bit). Neither of them are appropriate for this anime. I actually really like the intro (both the animation and the song), but it just doesn't fit the show. It's too upbeat. I think the intro should have mixed upbeat and depressing sections together (the animation does somewhat but the music doesn't, and even the animation leans on the more 'comedy scary' moments than actual horror).
The outro is just weird. I don't like the animation, the music, or the tone. It's a generic old-school trope explored to death (images of the two characters floating together in a nothingness sea) with a love story tone, which isn't appropriate for the anime (not at this early stage anyway).
I feel like if you cut both the intro and outro from the show and showed the version with them and the version without them to two different audience groups, the version without them would be better received. That's sad.