How do I tell Google my site has a German version without buying a .de domain?

You do not need a .de domain to tell Google about your German version. Publishing a /de/ subfolder with proper hreflang de-DE tags, localized metadata, and content is enough for Google to index and rank it. SEATEXT's Translation Agent handles the subfolder structure, hreflang tags, and sitemap entries so Google treats each language as its own localized entity.