Thank you for your suggestion, Xusheng.
I am not sure if the site language mapping may be a cause here, because after further investigation the similar error was noticed in a Cloud POS. The categories are visible but opening any of them results in the following error message: "We cannot process your request at this time. Please try again later" and products are not displayed.
I searched the LCS Raw logs and it seems that both errors (in site builder and Cloud POS) are connected with the following exception thrown on the Retail Cloud Scale Unit side:
An error occurred during the Retail Server Request. RequestUri: ang-ecom3fd46a7a560a724e2ret.cloud.retail.dynamics.com/.../SearchByCategory(channelId=5637145359,catalogId=0,categoryId=22565426194). RequestId: 4e1a0403-4b17-45e0-b22d-de99146d2c7a. Exception: Microsoft.Dynamics.Commerce.Merchandising.Search.Client.CommerceSearchException: Search failed with Forbidden and reason: Forbidden
at Microsoft.Dynamics.Commerce.Merchandising.Search.Client.SearchClient.<ExecuteSearchAsync>d__14`1.MoveNext()
--- End of stack trace from previous location where exception was thrown ---
at System.Runtime.ExceptionServices.ExceptionDispatchInfo.Throw()
at System.Runtime.CompilerServices.TaskAwaiter.HandleNonSuccessAndDebuggerNotification(Task task)
at Microsoft.Dynamics.Commerce.Merchandising.Search.Client.SearchClient.<SearchAsync>d__12`1.MoveNext()
--- End of stack trace from previous location where exception was thrown ---
at System.Runtime.ExceptionServices.ExceptionDispatchInfo.Throw()
at System.Runtime.CompilerServices.TaskAwaiter.HandleNonSuccessAndDebuggerNotification(Task task)
at Microsoft.Dynamics.Commerce.Runtime.SearchServices.Azure.ProductSearchAzureService.<MakeAzureProductSearchRequestAsync>d__60.MoveNext()
--- End of stack trace from previous location where exception was thrown ---
at System.Runtime.ExceptionServices.ExceptionDispatchInfo.Throw()
at System.Runtime.CompilerServices.TaskAwaiter.HandleNonSuccessAndDebuggerNotification(Task task)
at Microsoft.Dynamics.Commerce.Runtime.SearchServices.Azure.ProductSearchAzureService.<GetProductSearchResultsAsync>d__38.MoveNext()
--- End of stack trace from previous location where exception was thrown ---