Expose AppInstallManager product installation requests through a compiled cmdlet

Parent: #232

Dependencies and access restriction

Depends on #233, #234, #236. Implementation remains blocked until the supported-access gate and listed prerequisites are complete.

Microsoft documents AppInstallManager access as protected by a private capability restricted to Microsoft-developed apps. Do not bypass that restriction or treat runFullTrust/admin access alone as sufficient.

API scope

Supported StartProductInstallAsync and StartProductInstallForUserAsync overloads, including AppInstallOptions. Do not build on retired StartAppInstallAsync.

Acceptance criteria

• Bind documented product/catalog/identity/correlation inputs without hardcoded private values. Map supported overloads and options explicitly.
• Make current-user, specified-user and all-user intent unambiguous. Validate the supported user/privilege context; never auto-elevate or interpret a writable capability flag as proof of authorization.
• Account for target volume, repair, staging, storage preference, forced app restart, launch, pinning, toast and campaign options. Intrusive actions require explicit opt-in; document intentionally unsupported options and version gates.
• ShouldProcess precedes each request; -WhatIf submits no installation, entitlement or associated mutating work.
• Return typed request/item identities and observed initial state, not fabricated installation success. Support later monitoring without requiring it implicitly.
• Preserve async and native errors, partial multi-item results and cancellation semantics. No implicit entitlement acquisition or paid purchase.
• Document the supported post-first-sign-in context and the documented warning against use during OOBE.

Shared delivery requirements

Follow the parent epic's compiled-C# contract, user-scope and capability/version gates. Include deterministic Pester 6.2+ coverage, comment-based help, public documentation and unreleased notes in the same implementation PR. Use fail-closed fake adapters for side effects; no real installs, entitlement grants or settings changes in CI. Preserve original errors and distinguish unavailable, unknown, requested and completed outcomes.

Documented API references

• https://learn.microsoft.com/uwp/api/windows.applicationmodel.store.preview.installcontrol.appinstallmanager.startproductinstallasync
• https://learn.microsoft.com/uwp/api/windows.applicationmodel.store.preview.installcontrol.appinstallmanager.startproductinstallforuserasync
• https://learn.microsoft.com/uwp/api/windows.applicationmodel.store.preview.installcontrol.appinstalloptions

Start with parent issue #232 and dependencies #233, #234, and #236, then read the documented AppInstallManager product-install overloads and AppInstallOptions references. The implementation is complete when the compiled cmdlet, Pester 6.2+ tests, help, public documentation, and unreleased notes cover the stated validation, ShouldProcess, error, cancellation, and fail-closed adapter requirements without performing real installs.