### 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
strategy._tqm.send_callback(result.method_name, *result.args, **result.kwargs)
            elif isinstance(result, TaskResult):
                strategy.normalize_task_result(result)
                with strategy._results_lock:
                    strategy._results.append(result)
            elif isinstance(result, PromptSend):
                try:
                    value = display.prompt_until(
                        result.prompt,
                        private=result.private,
                        seconds=result.seconds,
                        complete_input=result.complete_input,
                        interrupt_input=result.interrupt_input,
                    )
                except AnsibleError as e:
                    value = e
                except BaseException as e:
                    
                    try:
                        raise AnsibleError(f"{e}") from e
                    except AnsibleError as e:
                        value = e
                strategy._workers[result.worker_id].worker_queue.put(value)
            else:
                display.warning('Received an invalid object (%s) in the result queue: %r' % (type(result), result))
        except (IOError, EOFError):
            break
        except queue.Empty:
            pass
def debug_closure(func):