Windows 10 upgrades using external hard drive

In a Command Prompt (Admin) or Powershell (Admin) run:

powercfg -h off

That will turn off hibernation and Windows fast startup and delete the system file used for hibernation which might give you some extra space. And the command:

compact /compactos always

Will ensure the OS is installed in the compacted state, and if it is not will get you some extra space.

I have two 32GB eMMC computers, they both have SD Cards inserted that I transfer user data files too. Both of them have over 10GB left in the 32GB eMMC. Also, unallocated space for the recovery partition is not required. No recovery partition at all is required if you don't want it. The "HDD" or "SSD" can have nothing but a System Reserved (or EFI System) partition that it boots from, which does need something like 50MB of free space in the partition itself, and the rest of the drive can be filled to the end with the OS partition and the upgrade will still finish as long as it can update the partition the computer boots from. On many installs the "Recovery Partition" is just a Recovery folder on the root of C: drive.

I tried both powercfg -h off and powercfg.exe -h off from the Command Prompt (Admin) and neither of them had any effect. Any suggestions to make them work?

I have been able to carve out 2.56GB storage on my internal hard drive. I have now attached a 1TB external hard drive. When clicking on Windows 10 update I still get error message: Updates are available, but we temporarily need some space to install. Remove some things you don't need right now and we'll try again." What do I do now?

1) Open disk management > expand all columns so that you can view the full contents of each row > post an image into the thread>
Take Screenshot in Windows 10 General Tips Tutorials

2) Download and install the mini partition wizard (free edition) and post an image into the thread:
MiniTool Partition Wizard | Best partition magic alternative for Windows PC and Server

As requested, here is my disk management status:

And MiniTool Partition Wizard screen:

These are some Microsoft upgrade guides:
Windows 10 System Requirements Specifications | Microsoft
https://support.microsoft.com/en-us/...10-upgrade-faq
Windows 10 edition upgrade (Windows 10) | Microsoft Docs