Media: Ensure that uploaded images get a success notification by users with...

Media: Ensure that uploaded images get a success notification by users with `upload_files` capability.

There was an early `wp_die` that was preventing the success notification from being sent in the upload process. 

Fixes #44581.

Props pbiron, mikeschroder, joemcgill, rebasaurus, whyisjake.


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git-svn-id: https://core.svn.wordpress.org/trunk@47897 1a063a9b-81f0-0310-95a4-ce76da25c4cd