When you uploaded the file you choose the path, instead of using the name of the img, you could use the id of the current user (go to the user tab in explorer, you will have the user variable containing the id)
If you allow more than only jpg you may need to extract the extension to concatenate it (<user-id>+"."+<file-extension>).
I’m not sure to understand what do you mean for the Retrieve public url, it should return you an url. What do you have in the result of the action when you use it ?
Some users reported a bug on the action where it return a wrong URL (a specific one that support transformation, like resize, but all supabase plan doesn’t provide this service so it’s not working for everyone) but it always return something, the fix is in review and should be released soon