refactor: move backend files to backend/ directory

Reorganize project structure:
- backend/cmd/openteam/ — entry point
- backend/internal/ — core packages
- backend/middleware/ — HTTP middleware
- backend/router/ — route setup
- backend/wire/ — dependency injection
- backend/pkg/ — shared utilities
- backend/go.mod, go.sum — Go module files

Updated Makefile to work from backend/ directory.
Removed old lowercase makefile.

backend/internal/proxy/handlers.go

@@ -0,0 +1,49 @@
+package proxy
+
+import (
+	"net/http"
+
+	"github.com/gin-gonic/gin"
+)
+
+// HandleChat handles POST /v1/chat/completions
+func (g *Gateway) HandleChat(c *gin.Context) {
+	req, err := g.ParseRequest(c, "chat")
+	if err != nil {
+		g.writeError(c, http.StatusBadRequest, err.Error())
+		return
+	}
+
+	g.Dispatch(c, req)
+}
+
+// HandleMessages handles POST /v1/messages
+func (g *Gateway) HandleMessages(c *gin.Context) {
+	req, err := g.ParseRequest(c, "messages")
+	if err != nil {
+		g.writeError(c, http.StatusBadRequest, err.Error())
+		return
+	}
+
+	g.Dispatch(c, req)
+}
+
+// HandleResponses handles POST /v1/responses
+func (g *Gateway) HandleResponses(c *gin.Context) {
+	req, err := g.ParseRequest(c, "responses")
+	if err != nil {
+		g.writeError(c, http.StatusBadRequest, err.Error())
+		return
+	}
+
+	g.Dispatch(c, req)
+}
+
+// HandleModels handles GET /v1/models
+func (g *Gateway) HandleModels(c *gin.Context) {
+	// TODO: Return list of available models based on enabled channels
+	c.JSON(http.StatusOK, gin.H{
+		"object": "list",
+		"data":   []interface{}{},
+	})
+}