notifications/prompts/list_changed are sended? #804
Description
Describe the bug
When serving prompts from a database (no in-memory PromptCollection) and advertising prompts.listChanged = true, sending a manual notification with
SendNotificationAsync("notifications/prompts/list_changed", new { }) does not reach clients (MCP Inspector shows nothing). Other notifications (e.g., "notifications/message") do appear, so notifications in general work. The prompt list/get RPCs work fine too.
Expected behavior
Clients (MCP Inspector) should receive notifications/prompts/list_changed after the server advertises prompts.listChanged = true and sends the notification, so they can refresh their prompt list cache.
Additional context
SDK: ModelContextProtocol.Core 0.3.0-preview.4 (.NET 9)
Transport: .WithHttpTransport() + endpoints.MapMcp("/mcp").RequireAuthorization()
Prompts are DB-backed; we do not use a PromptCollection mirror in memory.