How can I log in as a user with nuxt.auth?

I currently have the following nuxt.auth configuration.

auth: {
  strategies: {
    cookie: {
      endpoints: {
        login: { url: '/api/login', method: 'post' },
      },
    },
  },
},

When login is ok, the response is in json format with the following data

{'user': 'Tlaloc-Es'}

On the login page I have the following code:

this.$auth
  .loginWith('cookie', {
    data: {
      email: this.user_email,
      password: this.user_password,
      remember: this.remember,
    },
  })
  .then((data) => {
     const response = data.data.data;
     this.$auth.setUser(response.user);
     console.log(response.user);
     console.log(this.$auth.loggedIn);
  });

The problem is this.$auth.loggedIn always returns false.

I guess that auth doesn't set the user as logged, but I don't know any other steps I need part of:

this.$auth.setUser(response.user);

After a call, logging in browser stores the following cookies:

auth._token.cookie -> true
session -> session token
auth.strategy -> 'cookie'
auth._token_expiration.cookie -> false

How can I set the user as logged?

EDIT

If I execute the logout this value

auth._token.cookie

turn to false, but the session still is stored and anyway

this.$auth.loggedIn

return false.

EDIT Another try:

auth: {
    redirect: {
      login: '/login',
      logout: '/login',
      home: '/',
    },
    strategies: {
      cookie: {
        cookie: {
          name: 'session',
        },
        user: {
          property: false,
          autoFetch: false,
        },
        endpoints: {
          login: { url: '/api/login', method: 'post' },
          logout: { url: '/api/logout', method: 'post' },
        },
      },
    },
  },


async signIn() {
      const succesfulLogin = await this.$auth.loginWith('cookie', {
        data: {
          email: this.user_email,
          password: this.user_password,
          remember: this.remember,
        },
      });
      if (succesfulLogin) {
        const response = succesfulLogin.data.data;
        await this.$auth.setUser({ user: response.user });
        console.log(this.$auth.loggedIn);
        //await this.$auth.logout();
      }
    },

This is after login:

reponse cookie

Thanks.

Finally works with the following configuration:

auth: {
  redirect: {
    login: '/login',
    logout: '/login',
    home: '/',
  },
  strategies: {
    cookie: {
      options: {
        httpOnly: true,
        path: '/',
      },
      user: {
        property: false,
        autoFetch: false,
      },
      endpoints: {
        login: { url: '/api/login', method: 'post' },
        logout: { url: '/api/logout', method: 'post' },
      },
    },
  },
},