Implement "Browse Product Catalog" (UC-010)

Problem Description

An engineering team building a .NET 10 Blazor application has derived their entity model at docs/entity_model.md and use case specification at docs/use-cases/UC-010-browse-product-catalog.md.

The project is structured as a .NET 10 Web Application using Vertical Slice Architecture under Features/.

Output Specification

Implement UC-010 end to end under Features/UC010_BrowseProductCatalog/:

1. Vertical Slice:
   • BrowseProductCatalogPage.razor & .razor.cs Blazor components.
   • BrowseProductCatalogQuery.cs & BrowseProductCatalogHandler.cs handling data fetching.
   • EF Core entity mapping for Product entity.
2. Business Rule Enforcement:
   • Enforce filtering of out-of-stock items per BR-010.

Do not create any test files — that is handled by separate testing skills.