[Pipeline Bug]: The validation pipeline doesn't install the dependencies declared in the manifests

Nobody has claimed this yet.

During validation, the dependencies declared in the manifests were neither installed nor appeared in the validation logs, causing certain packages requiring dependencies failed to pass the validation.

For example:
- https://github.com/microsoft/winget-pkgs/pull/429038
The validation pipeline didn't install the VCRedist dependencies, causing the installers run the VCRedist installers interactively, blocking silent installation.
- https://github.com/microsoft/winget-pkgs/pull/415645
```
2026-08-18 16:04:42.275 [CORE] Deployment operation #1: Windows cannot install package MicrosoftCorporationII.Windows365_2.0.1315.0_x86__8wekyb3d8bbwe because this package depends on a framework that could not be found. Provide the framework "Microsoft.WindowsAppRuntime.2" published by "CN=Microsoft Corporation, O=Microsoft Corporation, L=Redmond, S=Washington, C=US", with neutral or x86 processor architecture and minimum version 2.1.3.0, along with this package to install. The frameworks with name "Microsoft.WindowsAppRuntime.2" currently installed are: {}
2026-08-18 16:04:42.275 [FAIL] C:\__w\1\s\external\pkg\src\AppInstallerCommonCore\Deployment.cpp(259)\WindowsPackageManager.dll!52FB1959: (caller: 52ED6749) Exception(1) tid(1ea8) 80073CF3 Package failed updates, dependency or conflict validation.
```
Validation failed on x86 installer only, either due to the dependency `Microsoft.WindowsAppRuntime.2` not installed during validation, or there might be some issues with that package.

Start by tracing the validation pipeline's handling of dependencies declared in manifests, then compare its installation behavior and logs with the examples from pull requests 429038 and 415645. Done means declared dependencies are installed before validation, dependency installation is visible in the validation logs, and packages requiring those dependencies pass validation.

Written by the indexing model from the issue text.