You can right-click on any folder in the Explorer pane and select Zip and Download. To grab everything in your project directory, go to File > Open Folder and accept the default /home/user. Then, right-click on studio in Explorer and click Zip and Download.
When prompted to rebuild the environment, don’t do it, after you get your download, re-open /home/user/studio.
We’ll take this as a feature request to make it easier to download everything–so thanks for reporting!
Also, you can export to GitHub. Just be sure to add any files that contain keys to .gitignore (especially and including the .env file!).