I believe you're right that you can't download "delta" updates, but standalone OS installers/updaters can be downloaded.
Go to https://apps.apple.com/app/macos-big-sur/id1526878132 (for Big Sur), click "Get", use Software Update to monitor the download progress, then "rescue" the installer ("Install macOS Big Sur.app") from Applications folder.
Go to https://apps.apple.com/app/macos-big-sur/id1526878132 (for Big Sur), click "Get", use Software Update to monitor the download progress, then "rescue" the installer ("Install macOS Big Sur.app") from Applications folder.