Today I faced the same issue where my database was changed from Multi User to Single User mode and this was eventually stopping me to publish database.
In order to fix this issue, I had to close all Visual Studio instances and run the below command in Sql Server query window -
USE [Your_Database_Name]; ALTER DATABASE [Your_Database_Name] SET MULTI_USER GO
This command has changed the DB from Single user to Multi User and afterwards, I was successfully able to publish.