Open your iPhone backup

Pick the folder called Backup. Paste %USERPROFILE%\Apple\MobileSync\Backup into the folder window's address bar to jump there. No backup yet? Make one in five minutes.

Why this page can't leak your messages

Your backup is read inside this browser tab. Nothing is uploaded.
This page loads no analytics or trackers, unlike the rest of the site.
Its security policy (connect-src 'self') tells the browser to refuse any connection to another server, so even a bug couldn't send your texts out. Developers can check the response headers.
Test it yourself: open this page, turn off Wi-Fi, then open your backup. It still works.