Refactor frontend script for clearer organization and reuse

[brawliscool]

Motivation

• Improve maintainability by organizing repeated UI state handling into reusable helpers.
• Reduce duplication in event handlers for dropzone, solve, export, and checkout flows.
• Make future feature additions (real solver integration, analytics) easier by centralizing behavior and lifecycle cleanup.

Description

• Introduced setElementVisibility, clearSolveTimeout, and updateUpgradeModalVisibility helpers to centralize DOM visibility and timeout cleanup.
• Extracted behaviors into focused functions: bindDropzoneEvents, solveCurrentImage, triggerTextDownload, requireSolutionForExport, handleStripeCheckout, getDemoSolution, and consumeQueryParam.
• Replaced inline event logic with calls to the new functions for dropzone binding, solve button, export buttons, and Stripe checkout buttons.
• Simplified URL query-parameter handling and consolidated final URL cleanup; all changes are in script.js.

Testing

• Ran a syntax check with node --check script.js, which succeeded.
• Verified the file compiles without parse errors after the refactor (syntax check above).

---

Codex Task