Refactor error handling to use anyhow throughout codebase

Switch all custom error types and handler signatures from `Box<dyn
std::error::Error + Send + Sync>` to `anyhow::Result`. Add anyhow as a
dependency. Fix typos and update function names for consistency.

Cargo.lock

@@ -368,6 +368,7 @@ dependencies = [
 name = "book_bot"
 version = "0.1.0"
 dependencies = [
+ "anyhow",
  "axum",
  "axum-prometheus",
  "base64",