Other applications menu doesn't show all applications

Not to be confused with #397, this is a separate issue.
I have a Docker Windows 11 VM setup, and currently the apps list looks like this when going on the Settings app:

However, WinApps setup lists these:

Some apps are missing, most importantly for me Affinity Designer, Affinity Photo and PyCharm. To note, I installed the Affinity programs using their default installer and PyCharm using JetBrains Toolbox. I looked a bit in the code and in ExtractPrograms.ps1 it seems it searches a path in the Registry which doesn't contain all installed apps (HKLM:\SOFTWARE\Microsoft\Windows\CurrentVersion\App Paths\).

The Uninstall folder also under CurrentVersion includes more apps and most have an entry called InstallLocation, but some leave it empty:

Also, the only way I found to get a list that includes PyCharm is using the Get-Package cmdlet, but I couldn't find a way to get an install path from the output:

PS C:\Users\Anna> Get-Package

Name                           Version          Source                           ProviderName
----                           -------          ------                           ------------
Mozilla Firefox (x64 en-CA)    134.0.2                                           Programs
Mozilla Maintenance Service    134.0.2                                           Programs
Office 16 Click-to-Run Exte... 16.0.18429.20044                                  msi
Office 16 Click-to-Run Lice... 16.0.18429.20132                                  msi
Microsoft 365 - en-us          16.0.18429.20132                                  Programs
Affinity Photo 2               2.5.6.2887                                        msi
Affinity Designer 2            2.5.6.2887                                        msi
PyCharm Professional           2024.3.2                                          Programs
JetBrains Toolbox              2.5.2.35332                                       Programs
Microsoft Edge Update          1.3.155.85                                        Programs
Microsoft Edge WebView2 Run... 100.0.1185.36                                     Programs
Microsoft OneDrive             23.038.0219.0001                                  Programs


PS C:\Users\Anna>

Start with ExtractPrograms.ps1 and its lookup of HKLM:\SOFTWARE\Microsoft\Windows\CurrentVersion\App Paths. Compare that source with the Uninstall registry entries and the Get-Package output described in the issue, including applications installed through Affinity's default installer and JetBrains Toolbox. Done means the Other applications menu discovers the missing applications without breaking existing entries.