Fix gamepad stick Y direction and overlapping paws

[hatrd]

Summary

• Invert stick Y values when applying SDL gamepad input to the Live2D model, while retaining raw axis state for diagnostics and replay.
• Hide the same-side stick paw while a gamepad button overlay is active in normal mode, then restore it on release. The explicit four-hands preference keeps its existing behavior.
• Add regressions for both stick directions, both shoulder buttons, analog triggers, and release behavior; update the Live2D audit expectation and test target linkage.

Validation

• Windows Release build with Cubism and warnings as errors.
• app-state and gamepad-state tests: 2 passed. Direct-input regressions ran; the virtual-gamepad portion skipped because a physical gamepad was connected.
• Native Cubism gamepad-sticks smoke check: assertions passed.