### 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
item_vars = {}
    if task.loop or task.loop_with:
        loop_var = result.get('ansible_loop_var', 'item')
        index_var = result.get('ansible_index_var')
        if loop_var in result:
            item_vars[loop_var] = result[loop_var]
        if index_var and index_var in result:
            item_vars[index_var] = result[index_var]
        if '_ansible_item_label' in result:
            item_vars['_ansible_item_label'] = result['_ansible_item_label']
        if 'ansible_loop' in result:
            item_vars['ansible_loop'] = result['ansible_loop']
    return item_vars
def results_thread_main(strategy):
    while True:
        try:
            result = strategy._final_q.get()
            if isinstance(result, StrategySentinel):
                break
            elif isinstance(result, DisplaySend):
                display.display(*result.args, **result.kwargs)
            elif isinstance(result, CallbackSend):
                for arg in result.args:
                    if isinstance(arg, TaskResult):
                        strategy.normalize_task_result(arg)
                        break