def send_notification(self, message):
    target_user_group = self.env.ref('module.group_name')

    target_users = self.env['res.users'].search(
        [('groups_id', '=', target_user_group.id)]
    )

    notification_ids = []
    for user in target_users:
        notification_ids.append((0, 0, {
            'res_partner_id': user.partner_id.id,
            'notification_type': 'inbox'}))

    self.message_post(body=message, message_type='notification', subtype='mail.mt_comment',
                      notification_ids=notification_ids)

you can do something like this here i'm getting all target users through a specific group and append notifications to them the notification will be shown in each user chat notification drop down list and also at the Discuss Home page

Hope it helped