@burnout426 I wondered if there was something about the directory the strange path points to, and I asked DuckDuckGo, "fedora what is the "/run/user/1000/doc" directory for"
I got this answer, which seems to clear things up:
"The /run/user/1000/doc directory is a portal that allows applications to access files outside of their sandbox in Fedora, particularly for applications installed via Flatpak. It is used to manage temporary file access for user applications."
However, it doesn't explain why Chromium and Opera can't reopen the file after the browser reopens. It remembers the path but can't open the image at that location. Presumably that's a feature (a "temporary" file) and not a bug. I'll have to trust Flatpak on that.
Thanks to all for your suggestions.