Update deployment for restructured API docs

[brookslybrand]

Summary

• sync API docs from their new docs/api location in the Remix monorepo
• resolve the generated-docs destination from this repository's root so it remains stable across source layout changes
• make cleanup paths independent of the caller's working directory

Testing

• bash -n sync.sh
• exercised sync.sh in a temporary checkout layout with a stubbed pnpm, verifying the source working directory, commands, output path, and cleanup behavior
• ran the full API docs generate, build, and prerender pipeline from the restructured Remix worktree

Dependency

Merge after remix-run/remix#11637. Until that lands, Remix release refs do not contain docs/api.

This also touches sync.sh, which is being updated for versioned snapshots in #2; the changes are compatible, but whichever PR merges second may need a rebase.