feat: support Responses to Chat (#5787)

* fix(openai): harden Chat-to-Responses compatibility

Add a shared Responses-to-Chat stream state machine and use it from the OpenAI relay path. Preserve assistant text alongside tool calls, bind tool argument deltas by output_index, map incomplete finish reasons, support reasoning/custom tool events, and buffer upstream SSE for non-stream Chat clients.

Add deterministic service tests and relay SSE tests for the conversion path.

Related to #5745.

* refactor: rename openaicompat to relayconvert for improved clarity

* feat(gemini): support responses request conversion

* feat: add responses to chat conversion support

* fix: harden responses chat conversion edge cases

relay/channel/claude/relay_claude_test.go

@@ -5,6 +5,8 @@ import (
 	"testing"
 
 	"github.com/QuantumNous/new-api/dto"
+	"github.com/QuantumNous/new-api/service"
+	"github.com/stretchr/testify/assert"
 	"github.com/stretchr/testify/require"
 )
 
@@ -12,6 +14,48 @@ func commonPointer[T any](value T) *T {
 	return &value
 }
 
+func TestResponseOpenAI2ClaudeToolUseInputIsObject(t *testing.T) {
+	tests := []struct {
+		name string
+		args string
+		want map[string]interface{}
+	}{
+		{name: "object", args: `{"q":"x"}`, want: map[string]interface{}{"q": "x"}},
+		{name: "empty", args: "", want: map[string]interface{}{}},
+		{name: "invalid", args: "{", want: map[string]interface{}{}},
+		{name: "null", args: "null", want: map[string]interface{}{}},
+		{name: "array", args: `["x"]`, want: map[string]interface{}{}},
+		{name: "string", args: `"x"`, want: map[string]interface{}{}},
+	}
+
+	for _, tt := range tests {
+		t.Run(tt.name, func(t *testing.T) {
+			msg := dto.Message{Role: "assistant"}
+			msg.SetToolCalls([]dto.ToolCallRequest{
+				{
+					ID:   "call_1",
+					Type: "function",
+					Function: dto.FunctionRequest{
+						Name:      "lookup",
+						Arguments: tt.args,
+					},
+				},
+			})
+			resp := service.ResponseOpenAI2Claude(&dto.OpenAITextResponse{
+				Id:    "chatcmpl_1",
+				Model: "gpt-test",
+				Choices: []dto.OpenAITextResponseChoice{
+					{Message: msg, FinishReason: "tool_calls"},
+				},
+			}, nil)
+
+			require.Len(t, resp.Content, 1)
+			assert.Equal(t, "tool_use", resp.Content[0].Type)
+			assert.Equal(t, tt.want, resp.Content[0].Input)
+		})
+	}
+}
+
 func TestFormatClaudeResponseInfo_MessageStart(t *testing.T) {
 	claudeInfo := &ClaudeResponseInfo{
 		Usage: &dto.Usage{},