refactor: replace RequestHandlerExtra with structured context types (#1467)

CLAUDE.md

@@ -144,7 +144,8 @@ When a request arrives from the remote side:
 2. **`Protocol.connect()`** routes to `_onrequest()`, `_onresponse()`, or `_onnotification()`
 3. **`Protocol._onrequest()`**:
     - Looks up handler in `_requestHandlers` map (keyed by method name)
-    - Creates `RequestHandlerExtra` with `signal`, `sessionId`, `sendNotification`, `sendRequest`
+    - Creates `BaseContext` with `signal`, `sessionId`, `sendNotification`, `sendRequest`, etc.
+    - Calls `buildContext()` to let subclasses enrich the context (e.g., Server adds `requestInfo`)
     - Invokes handler, sends JSON-RPC response back via transport
 4. **Handler** was registered via `setRequestHandler('method', handler)`
 
@@ -152,29 +153,42 @@ When a request arrives from the remote side:
 
 ```typescript
 // In Client (for server→client requests like sampling, elicitation)
-client.setRequestHandler('sampling/createMessage', async (request, extra) => {
+client.setRequestHandler('sampling/createMessage', async (request, ctx) => {
   // Handle sampling request from server
   return { role: "assistant", content: {...}, model: "..." };
 });
 
 // In Server (for client→server requests like tools/call)
-server.setRequestHandler('tools/call', async (request, extra) => {
+server.setRequestHandler('tools/call', async (request, ctx) => {
   // Handle tool call from client
   return { content: [...] };
 });
 ```
 
-### Request Handler Extra
+### Request Handler Context
 
-The `extra` parameter in handlers (`RequestHandlerExtra`) provides:
+The `ctx` parameter in handlers provides a structured context:
 
-- `signal`: AbortSignal for cancellation
-- `sessionId`: Transport session identifier
-- `authInfo`: Validated auth token info (if authenticated)
-- `requestId`: JSON-RPC message ID
-- `sendNotification(notification)`: Send related notification back
-- `sendRequest(request, schema)`: Send related request (for bidirectional flows)
-- `taskStore`: Task storage interface (if tasks enabled)
+**`BaseContext`** (common to both Server and Client), fields organized into nested groups:
+
+- `sessionId?`: Transport session identifier
+- `mcpReq`: Request-level concerns
+  - `id`: JSON-RPC message ID
+  - `method`: Request method string (e.g., 'tools/call')
+  - `_meta?`: Request metadata
+  - `signal`: AbortSignal for cancellation
+  - `send(request, schema, options?)`: Send related request (for bidirectional flows)
+  - `notify(notification)`: Send related notification back
+- `http?`: HTTP transport info (undefined for stdio)
+  - `authInfo?`: Validated auth token info
+- `task?`: Task context (`{ id?, store, requestedTtl? }`) when task storage is configured
+
+**`ServerContext`** extends `BaseContext.mcpReq` and `BaseContext.http?` via type intersection:
+
+- `mcpReq` adds: `log(level, data, logger?)`, `elicitInput(params, options?)`, `requestSampling(params, options?)`
+- `http?` adds: `req?` (HTTP request info), `closeSSE?`, `closeStandaloneSSE?`
+
+**`ClientContext`** is currently identical to `BaseContext`.
 
 ### Capability Checking