Ok so, on top of the Live Server vscode extension, you also have installed the browser extension following the setup guide. Now, Live server works in a specific way. When you start the server, it is indeed going to show the files and folder of the root project folder.
At the top, you can see that the URL is something like: http://127.0.0.1:5000, that's the Live Server address that you have to put in your web extension settings.
Besides, you have a specific URL that you use to access your web app locally such as http://myapp.test or http://localhost. That's the Actual Server Address in the Live Server web extension settings.
Once you start live server from vscode, you should visit your web app in a new tab or refresh it if there is already a tab. Please remember to refresh the web app URL after starting the Live Server, then you won't have to refresh the browser as long as the Live Server is up.