I have no idea where the Danmachi manga is at at the moment, I'm just read the light novels, which is currently at 14 translated in English with the 15th one coming out in a day or two. For reference, the anime is around the beginning to the middle of volume 10.
I really recommend reading the light novels for both Danmachi and especially for Bookworm. The Bookworm anime is barely into part 2 (of 5... maybe more overall arcs), which is like LN 4 of 25+. And at the pace the anime is going, it'll never catch up to the light novels and see those animated in their entirety, despite there already being a season 3 announced.
It's definitely a slow build of a story, but it does escalate, and while the first couple seasons give the smallest hints of magic and fantasy and etc, it's most most definitely there and a big part of things in later parts of the story. Part 2 has 4 volumes, and Part 3 is currently on volume 3 as far as English translations. Part 3 has 5 volumes of story, part 4 has 9 lol, and part 5 currently has 4 novels out and is no where close to where the webnovel rough draft finishes