test(tauri): stabilize background stdio timing

[su-fen]

Summary

• Stabilize the background stdio leak regression test under loaded Linux runners.
• Keep the background process alive for 15 seconds while allowing a 10-second detection window, so the test still proves the shell runner returns before the leaked stdio process exits.
• Capture and terminate the spawned background process after the assertion data is collected.

Root cause

The latest main workflow run 30447875966 failed only in Tauri Rust Check. The background stdio test returned correctly in about 4.06 seconds, but its fixed 3-second timing threshold was too strict for a loaded Linux runner.

Validation

• Full local CI matrix passed: Gateway, Gateway WebUI, GUI, Tauri, Docker, proto generation/checks, GUI/WebUI mirror check, and diff hygiene.
• Focused macOS regression test passed 10/10 consecutive runs.
• Ubuntu 24.04 shell_runner test suite passed 11/11 tests.
• Workflow-equivalent five-step Tauri Rust Check validation passed.
• git diff --check passed.