Can you recover original data from a screenshot that has been 'blacked out'?
Usually the PNG format does not support multiple layers. So when you draw over something, whatever was there before is lost.
However, the PNG format supports storage of an unlimited amount of metadata which is usually not displayed by image viewers. This feature is often used by image editors to add additional metadata to the image. One possible use-case is to store the undo-history of the image. This could mean that the previous version can be restored. To prevent this, make sure to set the exporting settings of your editor in a "export for web" mode which is supposed to strip all unnecessary data from the file. How to do this (and if it is even necessary) depends on the image editor.
Another possible faux-pas is to use an image blurring method which isn't 100% effective. You could, for example, accidentally set the opacity of your brush to almost but not completely 100%, which would mean that the section isn't recognizable by the human eye but might be made readable again by enhancing the contrast of the section. Another mistake is to use a filter which is reversible. I remember a case of a child-pornographer who got caught because he blurred out his own face with the "twirl" filter in Photoshop not realizing that when the same filter is applied in reverse, the image is restored to almost the original.
When you paint over a jpg or png file, you are not putting a sticker over the image, you are more ripping a hole on the image and filling the hole with ink.
Even on Photoshop, if you export the picture as jpg it will flatten the image, merging all layers together and destroying the original obscured area forever.
There's no way to reconstruct the original image. Taking a second screenshot will not add any security, just adding more steps to your job.
No, the security is no better. The typical formats used for screenshots (JPEG or PNG) are not image formats that support layers like say, a PSD does. When you add the green scribble, you're not adding a layer, you're replacing part of the image. The extra step, the screenshot-of-a-screenshot should give you an image file that's materially the same.
It's extra effort, but doesn't add any security value.