"TASK MANAGER" process is taking over a single-user mode database. What is it?

Had the same issue today, If you have not put your AUTO_UPDATE_STATISTICS ASYNC OFF, you will not be able to enter your database, you can solve this by putting your database offline. Important to know is that you need to set your deadlock priority to high, otherwise you will be deadlocked out of the command. Use following commands to get out of SINGLE user mode

SET DEADLOCK_PRIORITY HIGH

ALTER DATABASE [YourDBName] SET OFFLINE WITH ROLLBACK IMMEDIATE

Followed by

SET DEADLOCK_PRIORITY HIGH

ALTER DATABASE [YourDBName] SET ONLINE WITH ROLLBACK IMMEDIATE

Followed by

SET DEADLOCK_PRIORITY HIGH

ALTER DATABASE [YourDBName] SET MULTI_USER WITH ROLLBACK IMMEDIATE

I think the mystery finally got resolved:

Before you set the database to SINGLE_USER, verify the AUTO_UPDATE_STATISTICS_ASYNC option is set to OFF. When set to ON, the background thread used to update statistics takes a connection against the database, and you will be unable to access the database in single-user mode.

Stop the "system_health" extended events trace. It will be listed under

SQL Server Management Studio
-> [ServerName]
-> Management
-> Extended Events
-> Right-Click on 'System_health'
-> Hit Stop Session

Once the blocker are fixed, restart the session.