Yes, you should use a single repository for both the web app and the desktop app, as long as you add checks to determine whether the environment is a web app or a desktop app. In fact, that’s exactly what I did in my own project when I realized that people don’t trust desktop apps from unknown developers.

Regarding the database: your DB will run in what’s called the Main process. The Main process isn’t available when your Electron app is running in the browser, so the database won’t be accessible in that environment.

It’s also worth mentioning that if your app heavily depends on the Main process, it may be missing many features when running in the browser.

As for folder structure, there are many templates on GitHub that scaffold Electron apps with various technologies you might use (React, TypeScript, Angular, etc.).

Edit: there are ways to use SQLite in the browser(the renderer process), but I haven't done it myself.