Apple is not specifically preventing app updates as such for apps in the Downloads
folder.
macOS does however have extra security precautions in place when you're running applications from the Downloads
folder. One of those is "App Translocation".
"App Translocation" targets apps that haven't been moved after downloading, and makes so that when the app is executed, it will effectively be run from a read-only path that is randomly generated. This is to prevent evildoers from abusing legitimate software, that passes validation checks, and making that software load in their malicious code.
"App Translocation" does not happen after you move the app to the Applications
folder for example. You can also prevent it from happening by removing the quarantine attribute from the app, by running a command like this in the Terminal:
xattr -dr com.apple.quarantine ~/Downloads/Visual\ Studio\ Code.app
However, for most users I would recommend moving Visual Studio Code to the Applications
folder instead of trying to override security precautions.