Winget says package is already installed, when it isn't

Brief description of your issue

2 flavors of FFmpeg cannot be installed alongside each other, but the error message doesn't make sense and is confusing.

Steps to reproduce

• winget install --id 'Gyan.FFmpeg' --scope machine
• winget install --id 'Gyan.FFmpeg.Shared' --scope machine

Expected behavior

Either both packages install, or the second command explains that Gyan.FFmpeg.Shared cannot be installed alongside Gyan.FFmpeg (ideally, it would also explain that Gyan.FFmpeg.Shared is a superset of Gyan.FFmpeg, and propose to uninstall Gyan.FFmpeg automatically before installing Gyan.FFmpeg.Shared).

Actual behavior

The second command just says the package is already installed, which is not true and confusing. What's particularly problematic to me, is that the commands use IDs, so it doesn't make sense to me that 2 packages with different IDs cause this behavior.

Environment

Windows Package Manager v1.6.3133
Copyright (c) Microsoft Corporation. All rights reserved.

Windows: Windows.Desktop v10.0.22631.2715
System Architecture: X64
Package: Microsoft.DesktopAppInstaller v1.21.3133.0

Start by running the two winget install commands from the report against the stated package-manager environment, then trace the install conflict handling that produces the “already installed” message. Done means the second command either installs successfully or clearly explains the conflict between Gyan.FFmpeg and Gyan.FFmpeg.Shared, including any supported resolution.