Fix background startup and helper window movement

[Prgm-code]

What changed

• Start FatFingers with --background from autostart and keep all windows hidden.
• Ignore background-only second-instance launches.
• Allow dragging only on the frameless helper window and enlarge its drag strip.
• Preserve the helper size and position while the process remains active.
• Document the behavior and add tests for background launch detection and the drag region.

Root cause

Autostart used the same launch path as a manual invocation, so setup always called show_startup. The React drag strip already existed, but the helper did not have Tauri's core:window:allow-start-dragging permission. Reopening the helper also forced it back to 600x220.

Validation

• Frontend tests: 45 passed
• Rust tests: 37 passed
• Frontend production build passed
• cargo fmt --check and cargo check passed
• Frontend and Rust dependency audits passed
• Local Linux AppImage built and its runtime was verified

[coderabbitai]

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⚙️ Run configuration

Configuration used: defaults

Review profile: CHILL

Plan: Pro Plus

Run ID: 513b69e3-f4bf-42fd-9a92-009eeea9cadd

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