Reconcile the Application Builder lifetime model with Generic Host and #11415

[KlausLoeffelmann]

Objective

Research the current WinForms message-loop and ApplicationContext lifecycle, the Generic Host contracts, and #11415. Recommend one coherent ownership model for UI-thread startup, synchronization context, host start/stop, application exit, and failure propagation. Record alternatives and the smallest public contract needed by the other workstreams.

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.