feat(website): switch index filter URLs from querystring to path

Tag clicks on / pushState a category/group/subcategory path; on static
pages they fully navigate. Search and sort stay in querystring. Built-in
source tag has no data-url and stays as an in-page filter. The
isIndexDocument flag is captured at load time so toggling on the index
keeps working after pushState changes location.pathname.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>