fix(desktop): avoid sidecar health-check timeout on shell startup

[ysm-dev]

Fixes #13926

What does this PR do?

Desktop sidecar startup currently runs through an interactive login shell (-il). On some machines with heavier interactive shell init, this delays sidecar startup until the desktop health check times out.

This switches sidecar spawn to non-interactive login mode (-l -c) so login env setup is still applied without interactive shell hooks. It also fixes kill-channel handling so we only kill the child on an explicit kill signal, not when the channel closes.

How did you verify your code works?

• Reproduced the failure locally with bun dev:desktop (Health check timed out).
• Confirmed shell-related behavior with SHELL=/bin/sh bun dev:desktop.
• Verified startup works again after this change with default shell.
• Ran cargo check in packages/desktop/src-tauri.

[github-actions]

Thanks for your contribution!

This PR doesn't have a linked issue. All PRs must reference an existing issue.

Please:

1. Open an issue describing the bug/feature (if one doesn't exist)
2. Add Fixes #<number> or Closes #<number> to this PR description

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[ysm-dev]

Thanks for the catch — I opened #13926 and linked it in the PR description via Fixes #13926.