This doesn't solve the steam update issue but hibernating your PC instead of shutting it down would bypass the problem and is almost as good as shutting down your PC if you're concerned by noise and/or power usage.

You might have to enable hibernation manually depending on your PC, windows, updates, etc. See this guide from Microsoft.

This doesn't solve the steam update issue but hibernating your PC instead of shutting it down would bypass the problem and is almost as good as shutting down your PC if you're concerned by noise and/or power usage.

This works because hibernation saves the current running state of your PC to a file on the hard drive before shutting down. This file is then read back to RAM when you boot and your PC is restored to it's pre-hibernation state. Do still pause the download before hibernating to ensure steam properly finishes writing what it is currently downloading.

You might have to enable hibernation manually depending on your PC, windows, updates, etc. See this guide from Microsoft.