Possibly related: Mounted drives not available in some apps - #2 by rik
My theory is if in your “in-app file browser” if the current location is “a few levels deep” in the main storage then you don’t see the “top left” hamburger menu to select another drive. If you go to the root of the “main storage” then the hamburger appears and you can open the sidebar to select the SD card (or other drive)?