Refactor handler context to be transport- and handler-type-aware

The current RequestContext / ServerRequestContext design has a few rough edges that warrant a dedicated refactor:

1. Request vs notification context — Request handlers have request_id and meta, notification handlers do not. Currently request_id is optional (RequestId | None) on a single shared type, which loses type safety. Ideally these would be distinct types so request handlers get a context where request_id is always present, and notification handlers get one where it does not exist.

2. Transport-specific context — The request_context field on ServerMessageMetadata is typed as Any because the server layer is transport-agnostic (e.g. it is a Starlette Request for HTTP transports, None for stdio). A better design would let transports provide their own typed context that handlers can access without casting.

These two concerns are related — both point toward making the context type more precise depending on how and where a handler is invoked.

_{AI Disclaimer}

Commencez par suivre RequestContext et ServerRequestContext à travers les points d’entrée des handlers, puis examinez ServerMessageMetadata.request_context et les cas de transport mentionnés pour Starlette Request et stdio. Comparez la manière dont les handlers de requêtes et de notifications reçoivent le contexte et dont les valeurs propres au transport sont accessibles. Le travail est terminé lorsque les limites de types prévues et le comportement du transport sont définis sans dépendre de Any ni d’identifiants de requête optionnels.