Implement proper state management with Leptos signals

## Description
Replace the current JavaScript-based state management with proper Leptos reactive signals.

## Requirements
- Use Leptos signals for all state (current question, score, show result)
- Ensure reactive updates work correctly
- Remove JavaScript state management code
- Type-safe state updates

## Blocked By
- #32 (Leptos event handlers not working)

## Acceptance Criteria
- [ ] All state managed by Leptos signals
- [ ] UI updates reactively when state changes
- [ ] No JavaScript state management code
- [ ] All interactions type-safe

Start by resolving the dependency on issue #32, then inspect the existing JavaScript state management and the Leptos UI handling the current question, score, and result display. Done means those values use Leptos signals, UI changes reactively, JavaScript state management is removed, and interactions remain type-safe.

Written by the indexing model from the issue text.