Fix axum doctest examples; infer Json early responses; forward OperationIo early responses

[kieled]

Fixes #255.
Fixes #272.
Fixes #235.

This PR addresses two high-impact adoption pain points:

1. Docs/onboarding: doctest examples failed to compile

• The docs examples called axum::serve(...) which is feature-gated in axum (tokio + http1/http2). With axum used with default-features = false, axum::serve is not always available, causing doctest failures.
• The main aide::axum example also unnecessarily forced the /api.json route through IntoApiResponse even though it is not documented (added via .route, not .api_route).

Changes:

• Update doc examples in:
  • crates/aide/src/axum/mod.rs
  • crates/aide/src/redoc/mod.rs
  • crates/aide/src/swagger/mod.rs
  • crates/aide/src/scalar/mod.rs
    to avoid calling axum::serve in doctests.
• Use plain axum routing::get + IntoResponse for the non-documented /api.json handler in the aide::axum docs example.

2. OperationInput inference: early responses

• OperationIo with input_with = ... previously delegated operation_input but did not delegate OperationInput::inferred_early_responses, so early responses were silently dropped.
• axum::Json<T> did not provide inferred early responses, even though axum returns rejections before the handler body for invalid JSON and content-type mismatches.

Changes:

• OperationIo now forwards inferred_early_responses when input_with is used.
• axum::Json<T> now reports inferred early responses:
  • 400: failed to parse JSON
  • 415: missing/invalid Content-Type: application/json
  • 422: valid JSON but failed to deserialize into the target type

Tests:

• Added/extended tests covering:
  • OperationIo forwarding of inferred_early_responses
  • axum::Json<T> inferred early response status codes

Commands run:

• cargo test -p aide --doc --all-features
• cargo test --workspace --all-features
• cargo build --examples --all-features

(These changes should also reduce confusion seen in #278 and #265 by removing common docs-triggered failure modes.)

[jplatte]

Please split into at least two PRs (docs, inferred_early_responses).

[kieled]

Split per review request:

• docs: fix axum examples and doctests #286: docs/doctest fixes
• Fix inferred early responses for input_with and axum::Json #287: inferred_early_responses fixes (input_with forwarding + axum::Json)

This PR is superseded by those two.