Tighten PR 18 verification coverage

[ChristianPavilonis]

Summary

• assert explicit adapter route registrations instead of relying on non-404 responses behind wildcard fallbacks
• compare cross-adapter critical header values, not just header presence
• lint the integration test crate's test targets in CI with --all-targets

Verification

• cargo fmt --all -- --check
• cargo test-axum --test routes
• cargo test-cloudflare --test routes
• cargo test --manifest-path crates/integration-tests/Cargo.toml --test parity
• cargo clippy --manifest-path crates/integration-tests/Cargo.toml --all-targets -- -D warnings
• cargo clippy --workspace --all-targets --all-features -- -D warnings
• cargo test-axum
• cargo test-cloudflare
• cargo test-fastly