On the Edit page for a Post or Page, show an infobox with a list of Webmentions already sent

[artlung]

It could take design cue from the existing trackback infobox, visible if enabled in Screen Options

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Update:
Note that it does appear that they are saved to {$wpdb->prefix}posts.pinged and then are displayed in the Already pinged part of the above box, but it might be nice to see more detail for diagnostic purposes.