### Summary

The ansible-core 2.15 ignores handlers notified by another handlers when are more than one  case.

With the ansible-core 2.14, all cases of handlers notified by another handlers are runned.

### Issue Type

Bug Report

### Component Name

notify

### Ansible Version

```console
ansible [core 2.15.0]
  config file = /etc/ansible/ansible.cfg
  configured module search path = ['/home/user/.ansible/plugins/modules', '/usr/share/ansible/plugins/modules']
  ansible python module location = /usr/lib/python3.11/site-packages/ansible
  ansible collection location = /home/user/.ansible/collections:/usr/share/ansible/collections
  executable location = /usr/bin/ansible
  python version = 3.11.3 (main, Apr  5 2023, 15:52:25) [GCC 12.2.1 20230201] (/usr/bin/python)
  jinja version = 3.1.2
  libyaml = True
```


### Configuration

```console
CONFIG_FILE() = /etc/ansible/ansible.cfg
EDITOR(env: EDITOR) = vim
PAGER(env: PAGER) = less
```


### OS / Environment

Archlinux

ansible 7.6.0-1
ansible-core 2.15.0-1
ansible-lint 6.15.0.r45.g2fca3fe-2
python-ansible-compat 4.0.2-1

### Steps to Reproduce

<!--- Paste example playbooks or commands between quotes below -->
```yaml (paste below)
---
- name: Testing
  hosts: localhost
  tasks:
    - name: Trigger handlers
      debug:
        msg: Task 1
      changed_when: true
      notify: Handler 1
  handlers:
    - name: Handler 1
      debug:
        msg: Handler 1
      changed_when: true
      notify: Handler 2
    - name: Handler 2
      debug:
        msg: Handler 2
      changed_when: true
      notify: Handler 3
    - name: Handler 3
      debug:
        msg: Handler 3
```


### Expected Results

All handlers must be notified.

```console
PLAY [Testing] ********************************************************************************************************

TASK [Gathering Facts] ********************************************************************************************************
ok: [localhost]

TASK [Trigger handlers] ********************************************************************************************************
changed: [localhost] => {
    "msg": "Task 1"
}

RUNNING HANDLER [Handler 1] ********************************************************************************************************
changed: [localhost] => {
    "msg": "Handler 1"
}

RUNNING HANDLER [Handler 2] ********************************************************************************************************
changed: [localhost] => {
    "msg": "Handler 2"
}

RUNNING HANDLER [Handler 3] ********************************************************************************************************
changed: [localhost] => {
    "msg": "Handler 3"
}

PLAY RECAP ********************************************************************************************************
localhost                  : ok=5    changed=4    unreachable=0    failed=0    skipped=0    rescued=0    ignored=0
```

### Actual Results

Only the two first handlers were notified.

```console
PLAY [Testing] *************************************************************************************************

TASK [Gathering Facts] *************************************************************************************************
ok: [localhost]

TASK [Trigger handlers] *************************************************************************************************
changed: [localhost] => {
    "msg": "Task 1"
}

RUNNING HANDLER [Handler 1] *************************************************************************************************
changed: [localhost] => {
    "msg": "Handler 1"
}

RUNNING HANDLER [Handler 2] *************************************************************************************************
changed: [localhost] => {
    "msg": "Handler 2"
}

PLAY RECAP *************************************************************************************************
localhost                  : ok=4    changed=3    unreachable=0    failed=0    skipped=0    rescued=0    ignored=0
```


### Code of Conduct

- [X] I agree to follow the Ansible Code of Conduct
if original_task.loop or original_task.loop_with:
                            new_item_result = TaskResult(
                                task_result._host,
                                task_result._task,
                                result_item,
                                task_result._task_fields,
                            )
                            self._tqm.send_callback('v2_runner_item_on_ok', new_item_result)
                            if result_item.get('changed', False):
                                task_result._result['changed'] = True
                            if result_item.get('failed', False):
                                task_result._result['failed'] = True
                    if 'ansible_facts' in result_item and original_task.action not in C._ACTION_DEBUG:
                        
                        if original_task.delegate_to is not None and original_task.delegate_facts:
                            host_list = self.get_delegated_hosts(result_item, original_task)
                        else:
                            
                            self._set_always_delegated_facts(result_item, original_task)
                            host_list = self.get_task_hosts(iterator, original_host, original_task)
                        if original_task.action in C._ACTION_INCLUDE_VARS:
                            for (var_name, var_value) in result_item['ansible_facts'].items():
                                
                                
                                for target_host in host_list:
                                    self._variable_manager.set_host_variable(target_host, var_name, var_value)
                        else:
                            cacheable = result_item.pop('_ansible_facts_cacheable', False)
                            for target_host in host_list: