feat(aide): implement OperationInput/OperationOutput for axum_extra::either types

[kyrias]

No description provided.

[fallenmi]

Either* represents alternatives, but both new macros currently compose every branch as though all branches were active.

For inputs, operation_input calls each branch in sequence. An Either<Query<A>, Query<B>> therefore documents both parameter sets as simultaneous requirements (and overlapping names report DuplicateParameter), while axum-extra actually tries the branches in order and accepts the first successful extractor.

For outputs, concatenating inferred_responses drops valid alternatives when branches use the same status. Either<Json<A>, Json<B>> yields two 200 responses; set_inferred_response keeps the first and reports InferredResponseConflict for the second, so one runtime response schema is omitted.

Please preserve the alternative semantics. For same-status responses, merge the schemas/content (for example with oneOf) instead of dropping a branch. For parameter alternatives, OpenAPI cannot natively express mutually exclusive parameter sets, so either define and document a safe fallback or avoid a generic OperationInput implementation for unsupported combinations. Please add regression tests for distinct/overlapping query fields and same-status output variants.

Reviewed with OpenAI Codex and Anthropic Claude assistance.