I am curious whether there is an option within the Regular Labs plugin range to automatically pop-up all existing images on my website at once, so that the original image file is shown in a large format lightbox.
The Modals plugin does indeed work for pup-ups if all images are linked to the media file.
Incorrect. Modals can create modal links on all images, even if there is no link around them.
You just need to give them a classname.
Which - if they haven't yet - you could do either once with DB Replacer, or retroactively with ReReplacer.