The app
Silverbox has no account, no sign-in, and no analytics. It makes no network requests: it does not send reports about how you use it, it does not check for updates on its own, and it does not fetch metadata or artwork. Everything it shows comes from the collections you add.
Everything it writes stays on your Mac: the settings, your favorites and play history, and the local data folder with installed games, save backups, edited configs, launch logs and caches. A launch report (Copy as Markdown in the launch log) goes to the clipboard, for you to paste into a bug report if you choose.
Some things open other programs: the emulators, which Silverbox starts to play a game, and your web browser, when you click a link such as a game's Wikipedia article or an emulator's website. What those programs do is up to them and their own privacy policies.
This website
getsilverbox.app is a static site on GitHub Pages. It sets no cookies and runs no analytics. GitHub serves the pages and may keep its own server logs; see GitHub's privacy statement. The fonts come from Google Fonts, so your browser asks Google for them; see Google Fonts' privacy note.
Questions
Open an issue on GitHub.