Unfortunately that's not the case, I've tried it and it didn't work:

16/10/2024 15:43:48 - 	SignatureState     : InvalidCertificate
16/10/2024 15:43:48 - 	SignedBy           : vbcity.com LLC
16/10/2024 15:43:48 - 	Certificate Info   : 
16/10/2024 15:43:48 - 		-------------------------------------------------------
16/10/2024 15:43:48 - 		[Subject]       : CN=vbcity.com LLC, O=vbcity.com LLC, S=Washington, C=US
16/10/2024 15:43:48 - 		[Issuer]        : CN=Sectigo Public Code Signing CA R36, O=Sectigo Limited, C=GB
16/10/2024 15:43:48 - 		[Serial Number] : 42CAAC7D566FF22405D19B17290F33B2
16/10/2024 15:43:48 - 		[Not Before]    : 20/01/2022 00:00:00
16/10/2024 15:43:48 - 		[Not After]     : 19/01/2025 23:59:59
16/10/2024 15:43:48 - 		[Thumbprint]    : 588F681138B4F0DACC8214154B07BC8D73DC99F9
16/10/2024 15:43:48 - 
16/10/2024 15:43:48 - 	Supported Products : 
16/10/2024 15:43:48 - 		Microsoft.VisualStudio.Community
16/10/2024 15:43:48 - 			Version : [15.0,17.0)
16/10/2024 15:43:48 - 		Microsoft.VisualStudio.Community
16/10/2024 15:43:48 - 			Version : [17.0,18.0)
16/10/2024 15:43:48 - 
16/10/2024 15:43:48 - 	References         : 
16/10/2024 15:43:48 - 	Prerequisites      : 
16/10/2024 15:43:48 - 		-------------------------------------------------------
16/10/2024 15:43:48 - 		Identifier   : Microsoft.VisualStudio.Component.CoreEditor
16/10/2024 15:43:48 - 		Name         : Visual Studio core editor
16/10/2024 15:43:48 - 		Version      : [15.0,18.0)
16/10/2024 15:43:48 - 
16/10/2024 15:43:48 - Signature Details...
16/10/2024 15:43:48 - 	Extension is signed with an invalid certificate
16/10/2024 15:43:48 - 		(PartialChain)      : A certificate chain could not be built to a trusted root authority.
16/10/2024 15:43:48 - 		(RevocationStatusUnknown): The revocation function was unable to check revocation for the certificate.
16/10/2024 15:43:48 - 		(OfflineRevocation) : The revocation function was unable to check revocation because the revocation server was offline.
16/10/2024 15:43:48 - 

When I am online instead, the installation with /admin switch works flawlessly

We have already tried that and this really did not help.
 Our command is run in PowerShell run as SYSTEM user (not normal, nor with just Admin rights) while the Internet adapter is turned off:
 

& "C:\Program Files (x86)\Microsoft Visual Studio\2017\Professional\Common7\IDE\VSIXInstaller.exe" /admin "C:\TEST\GhostDoc Enterprise.v2022.2.22190.VS2017-VS2022.Extension.vsix"

We are sure there are no security policies involved, as the tests were also run on a Hyper-V VM freshly installed from a general ISO on an offline machine with an offline user profile.

From my point of view the application is trying to get the required Digital Signature and it does not find any on the computer and it cannot get it online (because no adapted ofc). The VS 2017 on which we are trying to install it also was installed using SYSTEM user - maybe that makes some of the certificates to be misplaced/

What I would like to turn Your attention to is some quirk that might actually work as a workaround. As I've already pointed out, when I run the installation while online, the Digital Signature is available, and when I run it offline it's invalid.

(Offline and online comparisson)
 

However, if I start-up the installation while online and cancel it, the Digital Signature is somehow retained and stored, so it can be use it regardless of being online or offline
 

My question is: can I export this certificate(s) somehow somehow and install it for future installations?
 How to check where it is stored? Where exactly should I install it on a fresh computer to work offline installations?
 (Certs and their certification path)