feat(workspace): add GET /branches endpoint

internal/workspace/handler.go

@@ -62,6 +62,7 @@ func (h *Handler) Mount(r chi.Router) {
 
 		r.Get("/worktrees", h.listWorktrees)
 		r.Post("/worktrees", h.createWorktree)
+		r.Get("/branches", h.listBranches)
 	})
 	r.With(auth).Route("/api/v1/worktrees/{wtID}", func(r chi.Router) {
 		r.Delete("/", h.deleteWorktree)
@@ -340,6 +341,25 @@ func (h *Handler) createWorktree(w http.ResponseWriter, r *http.Request) {
 	writeJSON(w, http.StatusCreated, toWorktreeResp(wt))
 }
 
+func (h *Handler) listBranches(w http.ResponseWriter, r *http.Request) {
+	c, err := h.caller(r)
+	if err != nil {
+		writeErr(w, r, err)
+		return
+	}
+	id, err := parseUUID(chi.URLParam(r, "wsID"))
+	if err != nil {
+		writeErr(w, r, err)
+		return
+	}
+	branches, err := h.ws.ListBranches(r.Context(), c, id)
+	if err != nil {
+		writeErr(w, r, err)
+		return
+	}
+	writeJSON(w, http.StatusOK, branchListResp{Branches: branches})
+}
+
 func (h *Handler) deleteWorktree(w http.ResponseWriter, r *http.Request) {
 	c, err := h.caller(r)
 	if err != nil {