TL;DR
Stop the Task Scheduler service and ensure no open handles for the C:\Program Files (x86)\Microsoft Visual Studio\Installer dir
Details
I just had the same problem, and even rebooting didn't help. So, I dug in!
Process Hacker revealed there was a lock on the following file by the System process:
C:\Program Files (x86)\Microsoft Visual Studio\Installer\resources\app\ServiceHub\Services\Microsoft.VisualStudio.Setup.Service\VSIXConfigurationUpdater.exe.
If I used Process Hacker to close the handle, it just immediately reopened again :/
I thought to check Task Scheduler (since it runs as SYSTEM in svchost), and sure enough there were tasks in there that run VSIXConfigurationUpdater.exe, even though they weren't actually running at that time.
So I stopped the Task Scheduler service, then used Process Hacker to close the handle on VSIXConfigurationUpdater.exe - and this time it didn't return! After ensuring there were no open handles on anything inC:\Program Files (x86)\Microsoft Visual Studio\Installer, the Visual Studio installer was able to update.