When using `--include-programs` Chocolatey CLI is not showing all software appearing in Programs and Features

### Checklist

- [x] I confirm there are no unresolved issues reported on the [Chocolatey Status page](https://status.chocolatey.org).
- [x] I have verified this is the correct repository for opening this issue.
- [x] I have verified no other issues exist related to my problem.
- [x] I have verified this is not an issue for a specific package.
- [x] I have verified this issue is not security related.
- [x] I confirm I am using **official**, and **not** unofficial, or modified, Chocolatey products.

### What You Are Seeing?

When the Azure DevOps Integration Tool for Office 2019 is installed, Chocolatey CLI is not listing it when the `--include-programs` option is used, even though the software is showing in Windows "Programs and Features" and "Installed Apps".

### What is Expected?

The Azure DevOps Integration Tool for Office 2019 software should show when `choco list --include-programs` is run. This can then be synced with a Chocolatey package using `choco sync`.

### How Did You Get This To Happen?

1. Install Azure DevOps Integration Tool for Office 2019 on a computer using the executable (i.e. not with Chocolatey CLI). The software is available in this [GitLab comment](https://gitlab.com/chocolatey/solutions/support-issues/-/issues/119#note_2356160586).
2. Open `appwiz.cpl` to see the software listed as installed within Windows Programs and Features.
3. Run `choco list -i` and notice the software is not listed as "not managed by Chocolatey" section.

Software installed in Programs and Features:


Not showing in the list of `choco list -i`:


`Get-UninstallRegistryKey` detects the software:

```powershell
PS C:\> Import-Module C:\ProgramData\chocolatey\helpers\chocolateyInstaller.psm1
PS C:\> Get-UninstallRegistryKey *DevOps*

BundleCachePath : C:\ProgramData\Package
Cache\{dc062c70-41d6-4aa4-8a97-3e997f481bee}\AzureDevOps_IntToolOffice2019_enu.exe
BundleUpgradeCode : {{A6D905CD-C46F-3CC5-B302-BCE967D6952C}}
BundleAddonCode : {}
BundleDetectCode : {}
BundlePatchCode : {}
BundleVersion : 17.12.35431.1
VersionMajor : 17
VersionMinor : 12
BundleProviderKey : {dc062c70-41d6-4aa4-8a97-3e997f481bee}
BundleTag : tfs_officeIntegration,1033
EngineVersion : 3.14.1.8722
DisplayIcon : C:\ProgramData\Package
Cache\{dc062c70-41d6-4aa4-8a97-3e997f481bee}\AzureDevOps_IntToolOffice2019_enu.exe,0
DisplayName : Azure DevOps Integration Tool for Office 2019
DisplayVersion : 17.12.35431.1
Publisher : Microsoft Corporation
ModifyPath : "C:\ProgramData\Package
Cache\{dc062c70-41d6-4aa4-8a97-3e997f481bee}\AzureDevOps_IntToolOffice2019_enu.exe"
/modify
NoElevateOnModify : 1
NoRemove : 1
QuietUninstallString : "C:\ProgramData\Package
Cache\{dc062c70-41d6-4aa4-8a97-3e997f481bee}\AzureDevOps_IntToolOffice2019_enu.exe"
/uninstall /quiet
UninstallString : "C:\ProgramData\Package
Cache\{dc062c70-41d6-4aa4-8a97-3e997f481bee}\AzureDevOps_IntToolOffice2019_enu.exe"
/uninstall
EstimatedSize : 95133
Resume : 3
Installed : 1
PSPath : Microsoft.PowerShell.Core\Registry::HKEY_LOCAL_MACHINE\SOFTWARE\Wow6432Node\Microsoft\
Windows\CurrentVersion\Uninstall\{dc062c70-41d6-4aa4-8a97-3e997f481bee}
PSParentPath : Microsoft.PowerShell.Core\Registry::HKEY_LOCAL_MACHINE\SOFTWARE\Wow6432Node\Microsoft\
Windows\CurrentVersion\Uninstall
PSChildName : {dc062c70-41d6-4aa4-8a97-3e997f481bee}
PSProvider : Microsoft.PowerShell.Core\Registry

AuthorizedCDFPrefix :
Comments :
Contact :
DisplayVersion : 17.12.35431
HelpLink :
HelpTelephone :
InstallDate : 20250227
InstallLocation :
InstallSource : C:\ProgramData\Package Cache\{29EE96FB-254C-3285-8FC6-624A46A57412}v17.12.35431\package
s\TFSOfficeIntegration\x64\Core\
ModifyPath : MsiExec.exe /I{29EE96FB-254C-3285-8FC6-624A46A57412}
Publisher : Microsoft Corporation
Readme :
Size :
EstimatedSize : 26704
SystemComponent : 1
UninstallString : MsiExec.exe /I{29EE96FB-254C-3285-8FC6-624A46A57412}
URLInfoAbout :
URLUpdateInfo :
VersionMajor : 17
VersionMinor : 12
WindowsInstaller : 1
Version : 286034535
Language : 1033
DisplayName : Azure DevOps Integration Tool for Office 2019 (x64)
PSPath : Microsoft.PowerShell.Core\Registry::HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows\Curre
ntVersion\Uninstall\{29EE96FB-254C-3285-8FC6-624A46A57412}
PSParentPath : Microsoft.PowerShell.Core\Registry::HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows\Curre
ntVersion\Uninstall
PSChildName : {29EE96FB-254C-3285-8FC6-624A46A57412}
PSProvider : Microsoft.PowerShell.Core\Registry

AuthorizedCDFPrefix :
Comments :
Contact :
DisplayVersion : 17.12.35431
HelpLink :
HelpTelephone :
InstallDate : 20250227
InstallLocation :
InstallSource : C:\ProgramData\Package Cache\{2B10AF18-2F80-364B-BA8E-041C541A1045}v17.12.35431\package
s\TFSOfficeIntegration\x64\enu\
ModifyPath : MsiExec.exe /I{2B10AF18-2F80-364B-BA8E-041C541A1045}
Publisher : Microsoft Corporation
Readme :
Size :
EstimatedSize : 724
SystemComponent : 1
UninstallString : MsiExec.exe /I{2B10AF18-2F80-364B-BA8E-041C541A1045}
URLInfoAbout :
URLUpdateInfo :
VersionMajor : 17
VersionMinor : 12
WindowsInstaller : 1
Version : 286034535
Language : 1033
DisplayName : Azure DevOps Integration Tool for Office 2019 Language Pack (x64) - ENU
PSPath : Microsoft.PowerShell.Core\Registry::HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows\Curre
ntVersion\Uninstall\{2B10AF18-2F80-364B-BA8E-041C541A1045}
PSParentPath : Microsoft.PowerShell.Core\Registry::HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows\Curre
ntVersion\Uninstall
PSChildName : {2B10AF18-2F80-364B-BA8E-041C541A1045}
PSProvider : Microsoft.PowerShell.Core\Registry
```

### System Details

* Operating System: 10.0.20348.0 Windows Server 2022
* Windows PowerShell version: 5.1.20348.2849
* Chocolatey CLI Version: 2.4.2
* Chocolatey Licensed Extension version: 6.3.1
* Chocolatey License type: Business
* Terminal/Emulator: Windows Terminal

Also confirmed on Chocolatey CLI 2.4.2 open-source, running on Windows 11 10..0.26100.0.

### Installed Packages

```bash
7zip 24.9.0
7zip.install 24.9.0
chocolatey 2.4.2
chocolatey.extension 6.3.1
chocolatey-agent 2.2.2
chocolatey-compatibility.extension 1.0.0
chocolatey-core.extension 1.4.0
chocolatey-license 2026.9.30.100
chocolatey-management-database 0.13.1
chocolatey-management-service 0.13.1
chocolatey-management-web 0.13.1
chocolatey-windowsupdate.extension 1.0.5
dotnet-8.0-aspnetruntime 8.0.8
dotnet-8.0-runtime 8.0.8
dotnet-aspnetcoremodule-v2 18.0.24201
jenkins 2.479.3
KB2919355 1.0.20160915
KB2919442 1.0.20160915
KB2999226 1.0.20181019
KB3033929 1.0.5
KB3035131 1.0.3
nexus-repository 3.71.0.6
sql-server-express 2022.16.0.1000
sql-server-management-studio 20.2.30
Temurin21jre 21.0.5.11
vcredist140 14.42.34433
```

### Output Log

```bash
https://gist.github.com/ryanrichter94/b28a3f5d33da16e41d5b7a3034376c55
```

### Additional Context

* [Zendesk ticket](https://chocolatey.zendesk.com/agent/tickets/25165).
* [GitLab issue](https://gitlab.com/chocolatey/solutions/support-issues/-/issues/119).
* [Clickup Spike Task](https://app.clickup.com/t/20540031/PROJ-2903)

It was suggested that perhaps the software installed in a user context and wouldn't show under a different user. I created a new account, `bob` and the software appears there so it is installed at the system level:


Start at the `choco list --include-programs` entry point and compare its installed-program discovery with the `Get-UninstallRegistryKey` output for the Azure DevOps Integration Tool. Reproduce on Windows using the listed command and registry entries; done means the software appears in the unmanaged-programs output and can be synchronized with `choco sync`.

Written by the indexing model from the issue text.