feat(website): add entrance animations and CSS-based filter bar visibility

Replace hidden attribute on filter-bar with opacity/transform transition
driven by a .visible class, allowing smooth fade-in/slide-down when a
filter is active. Add staggered hero-in keyframe animations to the page
title, subtitle, action buttons, and search box. Polish sortable table
headers with color transition on hover and active states.

Co-Authored-By: Claude <[email protected]>