Preserve multi-tool context in OpenAI messages continuation

Claude Code can send one assistant turn with multiple tool_use blocks followed by a user turn containing matching tool_result blocks. The OpenAI /v1/messages compatibility path trimmed continuation input to the last user turn plus adjacent tool outputs, which could leave a function_call_output without its earlier function_call when previous_response_id was attached.

This keeps all function_call items needed by retained function_call_output entries so the upstream Responses API can resolve every call_id.

Constraint: Applies only to the OpenAI /v1/messages -> Responses compatibility continuation path.

Rejected: Disable previous_response_id for all tool outputs | loses continuation and cache benefits for valid turns.

Confidence: high

Scope-risk: narrow

Directive: Do not trim function_call_output entries without preserving their matching function_call call_id context.

Tested: go test ./internal/service -run 'TestForwardAsAnthropic_(PreviousResponseIDKeepsMultiToolCallContext|AttachesPreviousResponseIDForCompatContinuation|OAuthPreservesClaudeCodeToolCallID)' -count=1

Tested: go test ./internal/service -run 'TestForwardAsAnthropic|TestApplyAnthropicCompatFullReplayGuard|TestOpenAICompat|Test.*ToolContinuation' -count=1

Tested: go test ./internal/pkg/apicompat -count=1

Related: #2337

backend/internal/service/openai_compat_model_test.go

@@ -480,6 +480,61 @@ func TestForwardAsAnthropic_AttachesPreviousResponseIDForCompatContinuation(t *t
 	require.Equal(t, "second", gjson.GetBytes(upstream.lastBody, "input.1.content.0.text").String())
 }
 
+func TestForwardAsAnthropic_PreviousResponseIDKeepsMultiToolCallContext(t *testing.T) {
+	t.Parallel()
+	gin.SetMode(gin.TestMode)
+
+	upstream := &httpUpstreamRecorder{}
+	svc := &OpenAIGatewayService{
+		httpUpstream: upstream,
+		cfg:          &config.Config{Security: config.SecurityConfig{URLAllowlist: config.URLAllowlistConfig{Enabled: false}}},
+	}
+	account := &Account{
+		ID:          1,
+		Name:        "openai-apikey",
+		Platform:    PlatformOpenAI,
+		Type:        AccountTypeAPIKey,
+		Concurrency: 1,
+		Credentials: map[string]any{
+			"api_key":  "sk-test",
+			"base_url": "https://api.openai.com/v1",
+		},
+	}
+
+	firstBody := []byte(`{"model":"claude-sonnet-4-5","max_tokens":16,"messages":[{"role":"user","content":"inspect files"}],"stream":false}`)
+	upstream.resp = openAICompatSSECompletedResponse("resp_first_tools", "gpt-5.3-codex")
+	firstRec := httptest.NewRecorder()
+	firstCtx, _ := gin.CreateTestContext(firstRec)
+	firstCtx.Request = httptest.NewRequest(http.MethodPost, "/v1/messages", bytes.NewReader(firstBody))
+	firstCtx.Request.Header.Set("Content-Type", "application/json")
+
+	firstResult, err := svc.ForwardAsAnthropic(context.Background(), firstCtx, account, firstBody, "stable-cache-key", "gpt-5.3-codex")
+	require.NoError(t, err)
+	require.NotNil(t, firstResult)
+
+	secondBody := []byte(`{"model":"claude-sonnet-4-5","max_tokens":16,"messages":[{"role":"user","content":"inspect files"},{"role":"assistant","content":[{"type":"tool_use","id":"call_one","name":"Read","input":{"file_path":"a.go"}},{"type":"tool_use","id":"call_two","name":"Read","input":{"file_path":"b.go"}}]},{"role":"user","content":[{"type":"tool_result","tool_use_id":"call_one","content":"package a"},{"type":"tool_result","tool_use_id":"call_two","content":"package b"},{"type":"text","text":"continue"}]}],"tools":[{"name":"Read","description":"read a file","input_schema":{"type":"object","properties":{"file_path":{"type":"string"}}}}],"stream":false}`)
+	upstream.resp = openAICompatSSECompletedResponse("resp_second_tools", "gpt-5.3-codex")
+	secondRec := httptest.NewRecorder()
+	secondCtx, _ := gin.CreateTestContext(secondRec)
+	secondCtx.Request = httptest.NewRequest(http.MethodPost, "/v1/messages", bytes.NewReader(secondBody))
+	secondCtx.Request.Header.Set("Content-Type", "application/json")
+
+	secondResult, err := svc.ForwardAsAnthropic(context.Background(), secondCtx, account, secondBody, "stable-cache-key", "gpt-5.3-codex")
+	require.NoError(t, err)
+	require.NotNil(t, secondResult)
+	require.Equal(t, "resp_first_tools", gjson.GetBytes(upstream.lastBody, "previous_response_id").String())
+
+	require.Equal(t, "function_call", gjson.GetBytes(upstream.lastBody, "input.1.type").String())
+	require.Equal(t, "call_one", gjson.GetBytes(upstream.lastBody, "input.1.call_id").String())
+	require.Equal(t, "function_call", gjson.GetBytes(upstream.lastBody, "input.2.type").String())
+	require.Equal(t, "call_two", gjson.GetBytes(upstream.lastBody, "input.2.call_id").String())
+	require.Equal(t, "function_call_output", gjson.GetBytes(upstream.lastBody, "input.3.type").String())
+	require.Equal(t, "call_one", gjson.GetBytes(upstream.lastBody, "input.3.call_id").String())
+	require.Equal(t, "function_call_output", gjson.GetBytes(upstream.lastBody, "input.4.type").String())
+	require.Equal(t, "call_two", gjson.GetBytes(upstream.lastBody, "input.4.call_id").String())
+	require.Equal(t, "continue", gjson.GetBytes(upstream.lastBody, "input.5.content.0.text").String())
+}
+
 func TestForwardAsAnthropic_ReplaysWithoutContinuationWhenPreviousResponseMissing(t *testing.T) {
 	t.Parallel()
 	gin.SetMode(gin.TestMode)