SetupMode is not a Windows variable that you can safely change with PowerShell. It is a UEFI firmware state, exposed to Windows through the Secure Boot variables. In particular, SetupMode=False is what you want on a PC that has Secure Boot keys enrolled.
Your two results are consistent with a normal Secure Boot configuration:
SecureBoot = True means the firmware is currently enforcing Secure Boot.
SetupMode = False means the firmware is not in UEFI "setup mode", meaning the platform is operating with its Secure Boot key hierarchy provisioned rather than waiting for keys to be installed.
So I would not try to change SetupMode to True. Doing so is not the next logical step, and there is no supported PowerShell command such as Set-SecureBootUEFI SetupMode True. The documented Set-SecureBootUEFI cmdlet can write certain UEFI Secure Boot variables, but SetupMode is controlled by the firmware as a consequence of the platform key state. It is not an ordinary Boolean setting that Windows can simply flip.
Microsoft's recent Secure Boot work involves replacing older UEFI certificates with newer certificates, and there are several separate pieces involved: the Platform Key (PK), Key Exchange Key (KEK), allowed-signature database (db), and the Secure Boot firmware variables/certificates. Updating one certificate does not necessarily mean that the firmware has completed the entire new Secure Boot certificate/key transition.
I would check the actual Secure Boot configuration rather than trying to alter SetupMode. In an elevated PowerShell window, run:
Confirm-SecureBootUEFI
Then run:
Get-SecureBootUEFI -Name PK,KEK,db,dbx
The second command will return binary data rather than a particularly useful human-readable description, so it is not necessarily the best diagnostic by itself.
An easier first check is to run:
msinfo32
Under System Summary, look for:
BIOS Mode Secure Boot State
Normally, you would expect:
BIOS Mode: UEFI Secure Boot State: On
If those say UEFI and On, then the PC is already booting with Secure Boot enabled. In that situation, SetupMode=False is not evidence of a problem. In fact, changing SetupMode to True would generally indicate moving the firmware into a state where Secure Boot keys can be provisioned, which is not what you normally want on a functioning Secure Boot system.
Btw. if by "will not reboot in Secure Mode" you mean that HP's firmware/Windows process is supposed to perform a Secure Boot certificate update and the machine refuses to complete that reboot/update, that is a different problem from Windows simply reporting Secure Boot as enabled. SecureBoot=True does not by itself prove that the particular Microsoft certificates HP was trying to install are present in the firmware's db database.
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hth
Marcin