How could I add button next to "edit image" button in "Attachment Details"
This is the location I would like to add button, Do you have any recommend?
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I would recommend that you begin by having a look at a question asked more recently here.
The best option would be to create a custom plugin so that the WP core doesn't get affected. Editing core files is never a good idea, plus you would lose any changes when updating WP.