Description of the need
If you ever set the Default picture on admin/config/people/settings, then you could have an impression the settings in the next section for Picture display style would apply to the default picture.

Unfortunately, it's not true as the HTML-code always shows:
<img src="http://in.docksal.site/files/pictures/default_image.png" alt="Backdrop CMS's picture" title="Backdrop CMS's picture">
for the default picture. However, if a user uploads his/her own picture, then the image style kicks in:
<img src="http://in.docksal.site/files/styles/thumbnail/public/pictures/picture-1-1614678151.png" alt="Backdrop CMS's picture" title="Backdrop CMS's picture">
Proposed solution
I don't see any reasons for the style selected in Picture display style section not to be applied for also the default picture. If you, guys, support this feature request, then I could offer a respective PR.
Recent comments
Hi ian, so, in your case all the other admin pages work fine, including the status page, only admin/reports/updates fails? But you can access admin/reports? Weird... I...
Update Report thows "Access denied You are not authorized to access this page."
The File (Field) Paths module should be able to move existing files. I've not tested it, but the module description says: Retroactive updates - rename and/or move...
Moving from /files into subdirectories
Yes indeed. We are exploring a few other more costly options, but as we are a low-resource start-up, we could save a lot of money by integrating Backdrop, CiviCRM and Ubercart for our membership...
UberPOS for Backdrop?