If each user can have many settings and each setting can belong to many users then the following is correct database design. A setting should belong to a setting type and therefore I've moved the foreign key to the settings table.

    Schema::create('users', function (Blueprint $table) {
        $table->increments('id');
        $table->string('firstname');
        $table->string('surname');
        $table->string('address')->nullable();
        $table->string('city')->nullable();
        $table->string('country')->nullable();
        $table->string('postcode')->nullable();
        $table->string('email')->unique();
        $table->string('password');
        $table->rememberToken();
        $table->timestamps();
    });

    Schema::create('settings', function (Blueprint $table) {
        $table->increments('id');
        $table->string('value');
        $table->timestamps();

        $table->integer('type_id')->unsigned();
        $table->foreign('type_id')->references('id')->on('setting_types');
    });

    Schema::create('setting_types', function (Blueprint $table) {
        $table->increments('id');
        $table->string('name');
        $table->timestamps();
    });

    Schema::create('users_settings', function (Blueprint $table) {
        $table->timestamps();

        $table->integer('user_id')->unsigned();
        $table->integer('setting_id')->unsigned();

        $table->foreign('user_id')->references('id')->on('users');
        $table->foreign('setting_id')->references('id')->on('settings');
    });

On your User::class add the relationship:

    public function settings()
    {
        return $this->belongsToMany(Setting::class, 'users_settings');
    }

On your SettingType::class add the relationship:

    public function settings()
    {
        return $this->hasMany(Setting::class, 'type_id');
    }

On you Setting::class add the relationships:

    public function type()
    {
        return $this->belongsTo(SettingType::class, 'type_id');
    }

    public function users()
    {
        return $this->belongsToMany(User::class, 'users_settings');
    }

To get the json you wanted, you could do:

$settings = Setting::with(['users', 'type'])->get();

return response()->json($settings);