A web site is sandboxed and cannot execute any external scripts – it is confined to the browser. But it can issue HTTP requests to a server. A server is not necessarily “a machine in some data center”, but more generally “any process that listens on some port and speaks HTTP”.
Because the JavaScript in the browser sandbox and the Python code can only communicate if the JS sends a HTTP request to a web server that then runs the Python code, you need a server. It is very easy to create a simple Python web server, e.g. with frameworks like Flask. They don't share variables, but they can transfer messages. The message then includes any necessary data. Often, the JS code would send an Ajax POST request with JSON-encoded data, and the server responds with another JSON document that contains the results.
But how can that work without an internet connection? It is possible to run the server on the same computer as the browser. The server then listens on localhost, and no real network requests are made. For example, when I develop a site with static HTML files I often start a simple server with python3 -m http.server -b localhost 8080. I can connect to the server by navigating to http://localhost:8080/ in my browser.
Instead of a static file server, you would run your Python server on some port. Your users would then install your Python software and launch the server, then open the correct address in the browser to load the GUI.
