go-sdk: fix context propagation through SDK calls and add prompt passthrough

[Copilot]

Per-request tool timeout contexts were silently dropped at the SDK layer — callSDKMethod always used the long-lived connection context c.ctx, so toolTimeout deadlines never actually cancelled backend calls. Additionally, backend prompts were never registered with the frontend SDK server, leaving prompts/list responses empty for all clients.

Context propagation (internal/mcp/)

• Added ctx context.Context to callSDKMethod, callSDKMethodWithReconnect, callTool, readResource, and getPrompt
• All six SDK session methods (ListTools, CallTool, ListResources, ReadResource, ListPrompts, GetPrompt) now receive the per-request context instead of c.ctx
• SendRequestWithServerID forwards ctx to both the plain JSON-RPC and SDK paths

// Before: tool timeout deadline silently dropped
result, err = c.callSDKMethodWithReconnect(method, params)

// After: deadline propagates to the SDK session call
result, err = c.callSDKMethodWithReconnect(ctx, method, params)

Prompt passthrough (internal/server/, internal/mcp/)

• Added registerPromptsFromBackend(ctx, serverID, conn) called from registerToolsFromBackend; prompts registered as serverID___promptName matching the tool convention
• Added BackendHasPromptsCapability() on Connection — checks session.InitializeResult().Capabilities.Prompts != nil before issuing prompts/list; guards against EOF responses on backends that don't declare prompt support, which would corrupt SDK session state and break subsequent tool calls
• Prompt handlers use per-session connections via GetOrLaunchForSession and forward ctx to the backend prompts/get call
• Failures in prompt registration are non-fatal (logged as warnings)

[Copilot]

Pull request overview

This PR fixes dropped per-request context propagation in the MCP go-sdk dispatch path (so toolTimeout deadlines can actually cancel backend calls) and adds backend prompt passthrough by registering backend prompts with the unified frontend SDK server.

Changes:

• Thread a per-request context.Context through SDK method dispatch (callSDKMethod*, callTool, readResource, getPrompt) and forward it from SendRequestWithServerID.
• Add Connection.BackendHasPromptsCapability() and use it when registering prompts to avoid issuing unsupported prompts/list calls on SDK sessions.
• Register backend prompts as <serverID>___<promptName> and add a prompt handler that forwards prompts/get to the appropriate backend connection.

Show a summary per file

File	Description
internal/server/tool_registry.go	Registers backend prompts into the unified frontend server and wires a prompts/get passthrough handler.
internal/mcp/connection.go	Adds prompt-capability detection and forwards per-request context through SDK reconnect + dispatch paths.
internal/mcp/connection_methods.go	Refactors SDK dispatch helpers to accept and use per-request context instead of the long-lived connection context.
internal/mcp/sdk_method_dispatch_test.go	Updates unit tests to pass request contexts into callSDKMethod.
internal/mcp/reconnect_sdk_test.go	Updates reconnect/SDK transport tests to pass request contexts into callSDKMethod*.

Copilot's findings

Tip

Add Copilot custom instructions for smarter, more guided reviews. Learn how to get started.

• Files reviewed: 5/5 changed files
• Comments generated: 1