Benchmark startup, shutdown, and repeated host lifetime resource stability

## Objective

Measure cold/warm startup, shutdown latency, allocations, retained memory, threads, handles, and repeated build/run/dispose cycles. Compare against a conventional `Application.Run` baseline and document acceptable overhead, one-time caches, and any leak indicators.

## 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.

No files, tests, or benchmark entry points are named. Start by locating the existing benchmark and test infrastructure, then identify how to compare the conventional Application.Run baseline with repeated build/run/dispose cycles. Done means recorded startup, shutdown, allocation, memory, thread, handle, and lifetime results, with decisions, acceptable overhead, cache behavior, leak indicators, and follow-up work documented.

Written by the indexing model from the issue text.