Depending on the website, you may have to navigate the CMS in order to get the permalink to the original file. If the uploaded images were shown on webpages, then it'd probably be too slow to load for most people's internet connection. I don't know about the inspector window in Firefox, but files can be downloaded of any format unmodified by right clicking the link and choosing Save As.

The inspector window was a workaround to save images that are unable to be right clicked and Save As'd, e.g. Instagram stories. Since the image is technically on a webpage, is there a way to extend the allowed load time before the image is shown in the inspector window - allowing for the full size image to load?

Also, even when opening the link address in a new tab it's downsized too.

Does the CMS allow access to the permalink in those circumstances?

Instagram is making it difficult; this has come up in other threads.

Are you clicking the image first to get the larger size to appear? That might be needed for the larger size (for example, 480x480 or 640x640) to get listed in Page Info/Media.

The distortion/scaling in the Media preview doesn't seem to affect Save As for me, I still get the expected square image, but I only tested with a single example.

I wonder whether the behind! extension might help? If there are a large number of images in the page, its list might be a bit overwhelming. https://addons.mozilla.org/firefox/addon/behind/