Startup script can't read registry

Question

I am trying to run a (PoSh) script as SYSTEM (i.e. at startup, via SCCM or otherwise) that needs to read some protected registry keys, and it can't see them.

A normal user doesn't have permission to see the keys. (Using a Mozilla key as an example, but there can be dozens under the "Tree" node.)

PS C:\> whoami
contoso\testuser
PS C:\>    $KeyPath = "HKLM:\SOFTWARE\Microsoft\Windows NT\CurrentVersion\Schedule\TaskCache\Tree\Mozilla"
PS C:\> $Key = Get-Item $KeyPath
Get-Item : Requested registry access is not allowed.

An admin user can see (but not change) the keys:

PS C:\> whoami
LocalComputer\administrator
PS C:\> $KeyPath = "HKLM:\SOFTWARE\Microsoft\Windows NT\CurrentVersion\Schedule\TaskCache\Tree\Mozilla"
PS C:\> Get-Item $KeyPath
Hive: HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows NT\CurrentVersion\Schedule\TaskCache\Tree


Name                           Property

Mozilla                        SD : {1, 0, 4, 140...}

But the SYSTEM account just doesn't see anything:

PS C:\> whoami
nt authority\system
PS C:\> $KeyPath = "HKLM:\SOFTWARE\Microsoft\Windows NT\CurrentVersion\Schedule\TaskCache\Tree\Mozilla"
PS C:\> Get-Item $KeyPath
Get-Item : Cannot find path 'HKLM:\SOFTWARE\Microsoft\Windows NT\CurrentVersion\Schedule\TaskCache\Tree\Mozilla'
because it does not exist.

SYSTEM has full control over the registry key and the parent key. What Admin sees (with permissions). This is what SYSTEM sees in the Registry.

How can SYSTEM not see it? How can I read this key via startup script (or other SYSTEM activity)?

Thanks.

Edit: As far as I can tell, this is is the case on ALL Win10 1809+, and not just a single machine.