Welcome to the Community!
There is no way to upload a folder, as the "browse" option for files will prompt you to drill down to the file level. That said, you can create a similar folder in the Online Storage prior to upload. Then open that folder and "Add Files". You can select your local files, then upload them all at once to that new folder. Or you can use drag-and-drop to place them in the new folder. These instructions should get you started.