refactor: split route handlers and keep TraceLayer request logging

[emostov]

Summary

• Move route handler logic and shared state out of router.rs into focused modules.
• Keep router.rs focused on route wiring.
• Preserve the existing TraceLayer::new_for_http() request logging layer.

Verification

• cargo fmt --check
• cargo test -p helloworld
• cargo clippy -p helloworld --all-targets -- -D warnings

Notes

• cargo test --all-targets currently fails on main in crates/e2e because CARGO_BIN_EXE_helloworld is unset; this PR does not change that unrelated harness behavior.