In your own WordPress MySQL database — Wyregraf stores and searches all vectors locally, and no external vector database or third-party search service is involved.
That means there is no extra account to create, no separate service bill, and your search index stays wherever your WordPress database lives. Standard site backups automatically include it. If you migrate or restore the site, Wyregraf recreates the vector search functions it needs in the new database automatically the next time a search runs.
One migration caveat: your profile API keys are stored encrypted with your site's security keys, so a migration that changes the salts in wp-config.php means re-entering the API keys in your profiles. The vectors themselves are unaffected.