After the message to “There is a new version” the download is started. I click install and then after some time I get the message "Unable to rename C:\Program Files\Sublime Text 3 to C:\Program Files\Sublime Text 3 (3211), it is being used by another process.
So I downloaded the seperated setup from the websites but this does not override ST3, this is installing ST4 next to ST3 which I do not want.
How to apply the update process in a correct way?
If you want you can simply uninstall Sublime Text 3, it won’t clear your user configuration. Otherwise it seems there a plugin or a separate process keeping Sublime Text 3 from closing before the updater is run.
The same error happened on my computer.
I found that it is the Kite service interrupting the update process.
Simply right-click the Kite icon on the taskbar and exit it before sublime updating. Then it will be fine.
Be careful that sublime may update more than once. Every time the update process end, sublime will restart and rise a new window to ask for an update. The Kite service will resume after the Sublime restart. So please remember to manually exit it again.