A combination I've always adored is the sound of live drums and piano, but thing is that it's hard to come by that combination without it being jazz, which requires a different mood for me. The only band that I really know of that does this is Big Scary.
I ran into this gem in r/animeshortfilms, and man does it scratch a good itch for me. The "talking pop" style that they have just wrecks me as well, I've just had this song on repeat for the last few days. They have an EP under Pop Shinanaide on Spotify, it took me a bit to figure that out.