Implement WinForms logging and unhandled-exception integration

## Objective

Integrate standard `ILogger` usage with suitable debug and file-provider guidance, UI-thread exception routing, structured context, startup/shutdown flushing, and privacy-safe defaults. Reuse ecosystem providers where possible rather than creating unnecessary WinForms-specific logging infrastructure.

## Completion guidance

- Keep the implementation focused on the objective while allowing the assignee to improve the approach based on research.
- Document important decisions, rejected alternatives, dependencies, and follow-up work.
- Add or update tests and documentation appropriate to the work.
- Verify locally and in CI where the task changes code or generated artifacts.

Start by researching the existing WinForms exception-routing and application-lifecycle entry points, then review standard ILogger usage and established file providers in the .NET ecosystem. Define completion through focused implementation, tests and documentation covering UI-thread exceptions, structured context, startup/shutdown flushing, privacy-safe defaults, and the documented design decisions.

Written by the indexing model from the issue text.