Make crate-level doc example compile-tested (0.1.1)

[azeemshaik025]

Converts the crate-level doc example from ignore to a compile-tested doctest, so docs.rs no longer shows the "This example is not tested" note and the example is verified on every build.

Changes

• src/lib.rs: crate-level example is now a real doctest — pub structs + a hidden main/async wrapper to satisfy the private-in-public rule (E0446) on stable rustc
• Bump 0.1.0 → 0.1.1
• CHANGELOG.md: 0.1.1 entry

Verification (on stable rustc 1.97.1, matching CI)

• cargo fmt --check — clean
• cargo clippy --all-targets -- -D warnings — clean
• cargo test — 19 tests pass; doctests: 1 passed, 2 ignored (the 2 remaining are on private internal types, not shown on docs.rs)
• cargo publish --dry-run — packages + verifies

The 2 still-ignored doctests are partial DSL-grammar snippets on private input types (ApiClientInput, EndpointDef); they don't render on the public docs page, so no badge.