I am afraid that you are correct - when you just click save, the project is saved in the browser's internal storage.
If you then choose to clear the browser's data including the option for "Cookies and other site and plugin data", that deletes your wade projects as well.
When you Download source code instead, you get a zip that you can save anywhere on your hard drive.
You are not the first to encounter this problem, and I think that we should make it clear, in the editor, what happens when you click Save. One of the things we're trying to do for the next version is to improve the user interface, and I think we will definitely include some sort of warning that appears when you click save (and that you can disable, otherwise it's going to get really annoying).
If at any point you have tried to build your project for Android, the project was sent to our servers for a cloud build. If that happened, we can try to recover it from our cloud build servers. In that case, just let me know the name of your project and I'll see if I can do anything about it.
Sorry for the inconvenience, I know it sucks to lose your work like this.
EDIT: One thing you could try, is using a file recovery program such as Recuva to try to undelete your files. They would have been stored in the browser's persistent storage directory. Please see here for the exact path (that depends on your OS).