Gate listTools/listPrompts/listResources/listResourceTemplates on server capability

[cliffhall]

Background

#1349 gated ManagedRequestorTasksState.refresh on the server's tasks capability so we don't fire tasks/list against servers that don't advertise it (which returned -32601 "Method not found" in the console on every connect to e.g. the NightRider example).

The same papercut exists in the other four list-fetching state managers:

• core/mcp/state/managedToolsState.ts — calls listTools
• core/mcp/state/managedPromptsState.ts — calls listPrompts
• core/mcp/state/managedResourcesState.ts — calls listResources
• core/mcp/state/managedResourceTemplatesState.ts — calls listResourceTemplates

Almost every server advertises tools/resources/prompts so the issue doesn't show up in practice today, but a "tools-only" server (or a "resources-only" server) would surface -32601 errors in the console on every connect — same root cause, same fix shape.

Screenshot

Scope

Add the same capability gate to each of the four state managers:

if (!client.getCapabilities()?.tools) {
  this.tools = [];
  this.dispatchTypedEvent("toolsChange", this.tools);
  return this.getTools();
}

(swap tools/prompts/resources per file).

Resource templates are gated on capabilities.resources (the MCP spec doesn't define a separate resourceTemplates capability — listResourceTemplates is part of the resources surface).

Tests

Mirror the two new tests added in #1349's managedRequestorTasksState.test.ts:

• Existing tests need their FakeInspectorClient to be constructed with the relevant capability so the live-path coverage is preserved.
• Add a "refresh skips listX when capability absent" test for each state manager.
• Add a "connect against an X-less server doesn't fire listX" test for each.

Same pattern in useManagedX.test.tsx peer files — they also need the capability set in beforeEach.

Out of scope

• Cleanup of the existing -32601 console noise in tests that intentionally probe unsupported methods (those are deliberate).