[JackyHsu-X]

When an AsyncOperation refresh raises a non-retryable error such as Forbidden, background polling fails without resolving the future. Completion callbacks never run, leaving callback-based callers waiting indefinitely.

Run background polling through a wrapper that stores ordinary polling exceptions on the future. This notifies existing callbacks and makes the original error available through result() and exception(). Preserve an already completed future, foreground polling behavior, and task cancellation.

Regression coverage includes both the base future and an actual AsyncOperation, plus completion racing with a polling failure and cancellation. On unchanged code, the two affected test modules have 4 failures and 22 passes; with the fix, all 26 pass.

Validation on Windows:

• Python 3.13, full google-api-core unit and asyncio suites: 1,643 passed, 1 skipped.
• Python 3.10 with the package's minimum-dependency constraints: 1,507 passed, 91 skipped.
• Python 3.13 without gRPC: 1,150 passed, 28 skipped.
• Combined package statement/branch coverage: 100%. Mypy, Flake8, and the applicable repository pre-commit hooks pass.

Cloud system tests, other packages in the monorepo, and other operating systems were not run locally.

• Make sure to open an issue before writing your code.
• Ensure the tests and linter pass.
• Code coverage does not decrease.
• Appropriate docs were updated (callback docstring).

Fixes #18862 🦕

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[gemini-code-assist]

Code Review

This pull request introduces a new _background_poll helper method in AsyncFuture to handle background polling failures by catching exceptions and setting them on the future, ensuring that registered callbacks are correctly invoked when background polling fails. It also includes comprehensive unit tests to verify error handling during background polling, cancelled polling, and foreground polling. There are no review comments to address, and I have no additional feedback to provide.