feat: configurable tool pricing, Sub2API channel, and alpha search billing

Add admin-configurable tool-call prices with cross-provider surcharge
settlement, Sub2API channel support, /v1/alpha/search relay, and usage-log
surcharge UI.

relay/constant/relay_mode.go

@@ -52,6 +52,8 @@ const (
 	RelayModeGemini
 
 	RelayModeResponsesCompact
+
+	RelayModeAlphaSearch
 )
 
 func Path2RelayMode(path string) int {
@@ -76,6 +78,8 @@ func Path2RelayMode(path string) int {
 		relayMode = RelayModeResponsesCompact
 	} else if strings.HasPrefix(path, "/v1/responses") {
 		relayMode = RelayModeResponses
+	} else if strings.HasPrefix(path, "/v1/alpha/search") {
+		relayMode = RelayModeAlphaSearch
 	} else if strings.HasPrefix(path, "/v1/audio/speech") {
 		relayMode = RelayModeAudioSpeech
 	} else if strings.HasPrefix(path, "/v1/audio/transcriptions") {

relay/constant/relay_mode_test.go

@@ -0,0 +1,22 @@
+package constant
+
+import (
+	"testing"
+
+	"github.com/stretchr/testify/assert"
+)
+
+func TestPath2RelayMode(t *testing.T) {
+	tests := []struct {
+		path string
+		want int
+	}{
+		{path: "/v1/alpha/search", want: RelayModeAlphaSearch},
+		{path: "/v1/alpha/search?foo=1", want: RelayModeAlphaSearch},
+	}
+	for _, tt := range tests {
+		t.Run(tt.path, func(t *testing.T) {
+			assert.Equal(t, tt.want, Path2RelayMode(tt.path))
+		})
+	}
+}