Fix race condition in BackgroundServiceExceptionTests

[lewing]

Problem

BackgroundService_AsynchronousException_StopAsync_ThrowsException is flaky (3 hits in 24 hours, #125550).

The test starts a BackgroundService that delays 100ms then throws, waits Task.Delay(200ms), and expects StopAsync to surface the exception. On loaded CI agents the 200ms isn't always enough for the exception to propagate through the host, so Assert.Throws sees no exception.

Assert.Throws() Failure: No exception was thrown
Expected: typeof(System.InvalidOperationException)

Fix

Replace the racy Task.Delay(200ms) with deterministic synchronization:

For StopHost behavior tests (StopAsync_ThrowsException, StopTwiceAsync_ThrowsException): Wait for IHostApplicationLifetime.ApplicationStopping, which fires after the host has captured the faulted service exception and called StopApplication(). This is the correct signal because it means the host has processed the exception and is ready to surface it on StopAsync.

For Ignore behavior test (IgnoreException_StopAsync_DoesNotThrow): Use a SignalingFailureService that signals a TaskCompletionSource before throwing. Since this test verifies StopAsync does not throw, we just need to know the service has faulted — no host-level processing is needed.

Both use a 10-second timeout as a safety net for CI.

Fixes#125550

[Copilot]

Pull request overview

Improves reliability of Microsoft.Extensions.Hosting unit tests by replacing timing-based delays with deterministic synchronization points when validating background service exception handling.

Changes:

• Replaced racy Task.Delay(...) waits with IHostApplicationLifetime.ApplicationStopping signaling for StopHost behavior tests.
• Updated the Ignore behavior test to use a signaling background service (SignalingFailureService) to deterministically coordinate when the failure path is reached.
• Added 10s WaitAsync timeouts as CI safety nets.

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[Copilot]

Pull request overview

Reduces flakiness in Microsoft.Extensions.Hosting unit tests by replacing a timing-based wait with a deterministic signal that the host has begun stopping after a background service fault, so StopAsync reliably surfaces the captured exception.

Changes:

• Replaced Task.Delay(200ms) with waiting on IHostApplicationLifetime.ApplicationStopping (with a 10s timeout) for StopHost-behavior tests.
• Updated comments in the Ignore-behavior StopAsync test (but the test still uses a fixed delay).

[svick]

/ba-g All failures seem to be iOS specific and not related to this PR.