The "Share" menu options in mac os seem to be limited to the "Share menu items" extensions under System settings. These offer actions like "Contact suggestions", "Add to reading list", "Airdrop", etc.: mostly actions that are limited to specific apps. I want to instead go to the shared item in the Finder, so that I have much more flexibility and control over what I want to do with it. Is there any way to add a new "Finder" item to the Sharing Extensions that lets me show the shared file in Finder?
A concrete example: I've just taken a screenshot using Shift+Cmd+4. It's saved to my Desktop folder, but how do I get to the file, so that I can move it to another location, or rename it, or whatever I want to do with the file? A thumbnail of the screenshot briefly appears in the lower right corner of the screen, and if I click on that, it opens in a window, which seems to be a Quick Look window. It has options at the top of the window including Share (icon) and "Open with Preview". Clicking the Share icon gives options like "Mail" and "AirDrop", i.e. the enabled Share extensions, but nothing about the Finder. I could open the Preview app, and then I have a few file manipulation options, but they're limited to a very small subset of what the Finder provides, since it's not a file manipulation app.
For this example, I could open the Finder separately and navigate to Desktop, then look for the screenshot among the files there. That assumes that I know where screenshots are saved (which currently I do, but it could change). For other contexts besides screenshots, I often don't know where to find the file that's being offered for sharing. In general, I want to get to the file itself in Finder, and all I have is a Share menu that offers me apps I don't want. Hence my main question, how to add extensions to the Share menu.
There are articles on the internet about "adding" extensions to the Share menu, which merely describe how to enable extensions that are already listed in System settings. So let me emphasize that I'm asking about adding extensions that are not already in those settings. Or some other way to show a file in the Finder via the Share menu.