fix: consolidate chat-completions compatibility fixes

- apply default mapped model only when scheduling fallback is actually used

- preserve reasoning in OpenAI-compatible output via reasoning_content and avoid invalid input function_call ids

backend/internal/pkg/apicompat/anthropic_responses_test.go

@@ -105,6 +105,7 @@ func TestAnthropicToResponses_ToolUse(t *testing.T) {
 	assert.Equal(t, "assistant", items[1].Role)
 	assert.Equal(t, "function_call", items[2].Type)
 	assert.Equal(t, "fc_call_1", items[2].CallID)
+	assert.Empty(t, items[2].ID)
 	assert.Equal(t, "function_call_output", items[3].Type)
 	assert.Equal(t, "fc_call_1", items[3].CallID)
 	assert.Equal(t, "Sunny, 72°F", items[3].Output)