I've done a fair amount of Advent of Code and I wouldn't say it's at all "focused" on this. The vast majority of the questions use hash tables and graph traversal as the full extent of their use of math/DS/algos.
There's always one or two puzzles every year that require some particular math/CS insight but most of them just need you to know BFS and/or how to write a parser.
Your examples are also not bad, but they seem to be primarily concerned with "getting familiar with a new programming language" in the context of writing a web server, which is one of the parts of programming I try to stay away from. Most of your examples require less familiarity with the language's features and more with libraries you might use, which is less interesting to me personally (then again, I'm a PL fan and I write compilers for a living).
Meanwhile, I like AoC because I've used language features to take the fairly straightforward potential implementations and write them more elegantly in the language I choose. e.g. I use Monads in Haskell, or use Rust's easy threading to parallelize solutions, etc.
For me, learning a new programming language is largely uninteresting unless it changes the fundamental "shape" I think in, rather than what the exact names of the libraries I use change to. e.g. I already know Java so I'm not really going to bother "learning" C#. I already know Python so I don't really bother diving deep into Ruby, etc. However, I learn Haskell, Rust, Forth, Erlang, Scheme, etc.