Scrinium Clipper by Jay

Requires Scrinium Unlimited, a one-time purchase in the Scrinium app for iPhone and iPad. Without it the extension signs in but refuses to clip.

Click the toolbar button and Scrinium Clipper captures the page you are reading — through your own browser session — and keeps a clean offline copy of the article, including the publisher's own metadata, in your own private iCloud database, where the Scrinium app picks it up. The badge shows saves waiting to upload.

No accounts, no third-party servers: sign in once with your Apple ID (on Apple's page), and everything you clip is stored in your private iCloud database; Scrinium's developer does not receive or access it.

Scrinium is an archive to search, not an inbox to clear.