Risking stating things you already know: If you upload an asset it is placed in the asset folder by default as far as I know, typically with the original file name appended some extra numbers. In that sense you don’t need to download the file, it is already in your assets folder. If you want to see exactly where it’s located and the file name you can enter edit mode to see what the actual file link is.
I don’t know any simple way to go directly to the file location, but one not so simple way is clicking on the file to open the pdf window, open the annotation page (the speech bubble looking button), and the clicking the file path link. That opens the pdf in the default pdf viewer. You could then open file location, save it to some other location, etc. But I haven’t really had the need to do this in my current workflow, so there might be easier ways that I haven’t seen.
If you want greater control over asset placement etc, I would recommend checking out the following post: Macros to improve assets management. I used that to create a pdf macro to easily open, reference and highlight files in Logseq that are located outside the assets folder.