chat: fix system prompt accumulation across conversation turns (#1076)

## Problem

In both `GetChatCompletionStream` and `GetChatCompletionCore`, the
system prompt was added as a `ResponseItem.CreateSystemMessageItem(...)`
in the input items list on every call. When `previous_response_id` is
used on follow-up turns, OpenAI already holds the full conversation
server-side — including the system message from turn 1. Every subsequent
turn (and every tool-call leg) was adding it again, causing the system
prompt to accumulate in context.

## Fix

Move the system prompt to `ResponseCreationOptions.Instructions` in
`CreateResponseOptionsAsync`, and remove the system message item from
both call sites.

Per the Azure OpenAI Responses API docs:
> "When using along with `previous_response_id`, the instructions from a
previous response will not be carried over to the next response. This
makes it simple to swap out system (or developer) messages in new
responses."

`Instructions` is stateless across turns by design — applied fresh each
call, never accumulated.

## Changes

- **`CreateResponseOptionsAsync`**: Added `string? systemPrompt`
parameter; sets `options.Instructions` from it (falling back to
`_Options.SystemPrompt`). Changed from `static` to instance method to
access `_Options`.
- **`GetChatCompletionCore`**: Removed `systemPrompt` parameter; input
list is always `[ResponseItem.CreateUserMessageItem(prompt)]`.
- **`GetChatCompletionStream`**: Same simplification — no system message
item in input list.
- **`GetChatCompletion`**: Passes `systemPrompt` to
`CreateResponseOptionsAsync` instead of downstream to
`GetChatCompletionCore`.

---------

Co-authored-by: copilot-swe-agent[bot] <198982749+Copilot@users.noreply.github.com>
Co-authored-by: BenjaminMichaelis <22186029+BenjaminMichaelis@users.noreply.github.com>

Author: BenjaminMichaelis

EssentialCSharp.Chat.Shared/Services/AIChatService.cs

@@ -54,9 +54,9 @@ public AIChatService(IOptions<AIOptions> options, AISearchService searchService,
         bool enableContextualSearch = false,
         CancellationToken cancellationToken = default)
     {
-        var responseOptions = await CreateResponseOptionsAsync(previousResponseId, tools, reasoningEffortLevel, mcpClient: mcpClient, cancellationToken: cancellationToken);
+        var responseOptions = await CreateResponseOptionsAsync(systemPrompt, previousResponseId, tools, reasoningEffortLevel, mcpClient: mcpClient, cancellationToken: cancellationToken);
         var enrichedPrompt = await EnrichPromptWithContext(prompt, enableContextualSearch, cancellationToken);
-        return await GetChatCompletionCore(enrichedPrompt, responseOptions, systemPrompt, mcpClient, cancellationToken);
+        return await GetChatCompletionCore(enrichedPrompt, responseOptions, mcpClient, cancellationToken);
     }
 
     /// <summary>
@@ -82,17 +82,12 @@ public AIChatService(IOptions<AIOptions> options, AISearchService searchService,
         bool enableContextualSearch = false,
         [System.Runtime.CompilerServices.EnumeratorCancellation] CancellationToken cancellationToken = default)
     {
-        var responseOptions = await CreateResponseOptionsAsync(previousResponseId, tools, reasoningEffortLevel, mcpClient: mcpClient, cancellationToken: cancellationToken);
+        var responseOptions = await CreateResponseOptionsAsync(systemPrompt, previousResponseId, tools, reasoningEffortLevel, mcpClient: mcpClient, cancellationToken: cancellationToken);
         var enrichedPrompt = await EnrichPromptWithContext(prompt, enableContextualSearch, cancellationToken);
 
-        // Construct the user input with system context if provided
-        var systemContext = !string.IsNullOrWhiteSpace(systemPrompt) ? systemPrompt : _Options.SystemPrompt;
-
         // Create the streaming response using the Responses API
 #pragma warning disable OPENAI001 // Type is for evaluation purposes only and is subject to change or removal in future updates. Suppress this diagnostic to proceed.
-        List<ResponseItem> responseItems = systemContext is not null
-            ? [ResponseItem.CreateSystemMessageItem(systemContext), ResponseItem.CreateUserMessageItem(enrichedPrompt)]
-            : [ResponseItem.CreateUserMessageItem(enrichedPrompt)];
+        List<ResponseItem> responseItems = [ResponseItem.CreateUserMessageItem(enrichedPrompt)];
 #pragma warning restore OPENAI001 // Type is for evaluation purposes only and is subject to change or removal in future updates. Suppress this diagnostic to proceed.
         var streamingUpdates = _ResponseClient.CreateResponseStreamingAsync(
             responseItems,
@@ -259,7 +254,8 @@ private async Task<string> EnrichPromptWithContext(string prompt, bool enableCon
     /// Creates response options with optional features
     /// </summary>
 #pragma warning disable OPENAI001 // Type is for evaluation purposes only and is subject to change or removal in future updates. Suppress this diagnostic to proceed.
-    private static async Task<ResponseCreationOptions> CreateResponseOptionsAsync(
+    private async Task<ResponseCreationOptions> CreateResponseOptionsAsync(
+        string? systemPrompt = null,
         string? previousResponseId = null,
         IEnumerable<ResponseTool>? tools = null,
         ResponseReasoningEffortLevel? reasoningEffortLevel = null,
@@ -270,6 +266,14 @@ private static async Task<ResponseCreationOptions> CreateResponseOptionsAsync(
         var options = new ResponseCreationOptions();
 #pragma warning restore OPENAI001 // Type is for evaluation purposes only and is subject to change or removal in future updates. Suppress this diagnostic to proceed.
 
+        // Set the system prompt via Instructions — this is stateless across turns when using previous_response_id,
+        // preventing accumulation of system messages in the conversation context.
+        var resolvedSystemPrompt = !string.IsNullOrWhiteSpace(systemPrompt) ? systemPrompt : _Options.SystemPrompt;
+        if (!string.IsNullOrWhiteSpace(resolvedSystemPrompt))
+        {
+            options.Instructions = resolvedSystemPrompt;
+        }
+
         // Add conversation context if available
         if (!string.IsNullOrEmpty(previousResponseId))
         {
@@ -318,17 +322,12 @@ private static async Task<ResponseCreationOptions> CreateResponseOptionsAsync(
 #pragma warning disable OPENAI001 // Type is for evaluation purposes only and is subject to change or removal in future updates. Suppress this diagnostic to proceed.
         ResponseCreationOptions responseOptions,
 #pragma warning restore OPENAI001 // Type is for evaluation purposes only and is subject to change or removal in future updates. Suppress this diagnostic to proceed.
-        string? systemPrompt = null,
         McpClient? mcpClient = null,
         CancellationToken cancellationToken = default)
     {
-        // Construct the user input with system context if provided
-        var systemContext = !string.IsNullOrWhiteSpace(systemPrompt) ? systemPrompt : _Options.SystemPrompt;
-
+        // Create the response using the Responses API
 #pragma warning disable OPENAI001 // Type is for evaluation purposes only and is subject to change or removal in future updates. Suppress this diagnostic to proceed.
-        List<ResponseItem> responseItems = systemContext is not null
-            ? [ResponseItem.CreateSystemMessageItem(systemContext), ResponseItem.CreateUserMessageItem(prompt)]
-            : [ResponseItem.CreateUserMessageItem(prompt)];
+        List<ResponseItem> responseItems = [ResponseItem.CreateUserMessageItem(prompt)];
 #pragma warning restore OPENAI001 // Type is for evaluation purposes only and is subject to change or removal in future updates. Suppress this diagnostic to proceed.
 
         const int MaxToolCallIterations = 10;