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

dto/channel_settings_test.go

@@ -0,0 +1,46 @@
+package dto
+
+import (
+	"testing"
+
+	"github.com/stretchr/testify/assert"
+	"github.com/stretchr/testify/require"
+)
+
+func TestAdvancedCustomValidateResponsesToChatConverterPath(t *testing.T) {
+	valid := &AdvancedCustomConfig{
+		Routes: []AdvancedCustomRoute{
+			{
+				IncomingPath: "/v1/responses",
+				UpstreamPath: "/v1/chat/completions",
+				Converter:    AdvancedCustomConverterOpenAIResponsesToOpenAIChatCompletions,
+			},
+		},
+	}
+	require.NoError(t, valid.Validate())
+
+	tests := []struct {
+		name         string
+		incomingPath string
+	}{
+		{name: "chat completions", incomingPath: "/v1/chat/completions"},
+		{name: "responses compact", incomingPath: "/v1/responses/compact"},
+	}
+
+	for _, tt := range tests {
+		t.Run(tt.name, func(t *testing.T) {
+			config := &AdvancedCustomConfig{
+				Routes: []AdvancedCustomRoute{
+					{
+						IncomingPath: tt.incomingPath,
+						UpstreamPath: "/v1/chat/completions",
+						Converter:    AdvancedCustomConverterOpenAIResponsesToOpenAIChatCompletions,
+					},
+				},
+			}
+			err := config.Validate()
+			require.Error(t, err)
+			assert.Contains(t, err.Error(), "converter does not match incoming_path")
+		})
+	}
+}