Preserve subprocesses after output stream errors

[desertaxle]

this PR keeps subprocesses running to completion when stdout or stderr forwarding fails, restoring compatibility with AnyIO 4.14.2.

Details

AnyIO 4.14.2 closes underlying subprocess pipe transports during cleanup. When Prefect's output consumer raises, that cleanup can terminate the flow process before it records a final state.

run_process now drains both pipes without forwarding their output and waits for the process to exit before re-raising the original streaming error. Cancellation continues through the existing termination path because the fallback handles only ordinary exceptions.

The regression emits one megabyte to each output stream after forcing a forwarding failure and verifies that the child still reaches completion. The focused process utility and runner tests pass with both AnyIO 4.14.1 and 4.14.2.

[codspeed-hq]

Merging this PR will not alter performance

✅ 8 untouched benchmarks
⏩ 1 skipped benchmark¹

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_{Comparing codex/anyio-4-14-2-compatibility (20bb144) with main (4b510e4)}

Footnotes

1. 1 benchmark was skipped, so the baseline result was used instead. If it was deleted from the codebase, click here and archive it to remove it from the performance reports. ↩