With the help of @Jared, I solved this problem.

I used localStorage to save the current state of the model and reload it when redirecting to another page.

const Model = (function () {

    let instance;

    let data = {
        isLogged: false,
    };

    function init_localStorage() {
        save_localStorage();
    }

    function load_localStorage() {
        let model = JSON.parse(localStorage.getItem('Model'));
        if (Object.keys(model).length === 0) {
            init_localStorage();
        }

        data = model;
    }

    function save_localStorage() {
        localStorage.setItem('Model', JSON.stringify(data));
    }

    function init() {
        load_localStorage();

        return {
            getIsLogged: function () {
                return data.isLogged;
            },
            setIsLogged: function (l) {
                data.isLogged = l;
            },

            saveData: function () {
                save_localStorage();
            }
        }
    }

    return {
        getInstance: function () {
            if (! instance) {
                instance = init();
            }
            return instance;
        }
    }
})();

Ultimately, I have two main functions: save... and load..., which read and save data from the localStorage object. As Jared said in the comments, JSON cannot stringify functions, so I created an object called data in which I store all the model's data (such as the isLogged variable).

Now, whenever I want to access the model's data, I first get its instance: let model = Model.getInstance(); Then I can access the method from the returned init function. When I request a Model instance, it first checks if the current instance is initialized. If not initialized, it calls the load_localStorage function to read data from localStorage and save it to the data variable.

Before redirecting to another page, I call the saveData function of the Model instance to save the data object to localStorage so that the redirected page can read the previously saved state.

In the HTML file, I included the js file like this: <script src="./../model/model.js"></script>.

I'm sure there are better solutions, maybe with more readable code, but this method works well enough for me :)