### Summary

The code that checks the connection + become details in a loop is not applying the become state on connections that have the `connected` attribute set to `True`. If connected is `True` the else block will just re-use the existing connection plugin which won't have the `become` details from the first task on it.

https://github.com/ansible/ansible/blob/27ce607a144917e6b9a453813a7df6bbc9ea2213/lib/ansible/executor/task_executor.py#L562-L572

Note there are some other bugs that mask this problem:

* ssh never sets `connected = True` so will always re-create the connection and subsequently the updated become info
* Using `ansible_connection=paramiko` also works because it never matches the connection `_load_name` of `paramiko_ssh`
* Redirected collections will most likely also mask the problem because of the load_name vs `ansible_connection` value check which is most certainly wrong.

The code needs to be updated to do a proper check for the connection name `self._connection._load_name != current_connection` to actually work properly with redirected plugins and aliased names like paramiko and paramiko_ssh. The code also needs to be updated so that if a connection is re-used then the become plugin needs to be added/deleted if necessary.

The connection should also be closed when being dropped as well.

### Issue Type

Bug Report

### Component Name

task_executor
connection
become

### Ansible Version

```console
$ ansible --version
ansible [core 2.14.0.dev0] (low-level-become e91a069260) last updated 2022/08/03 08:18:13 (GMT +1000)
  config file = None
  configured module search path = ['/home/jborean/.ansible/plugins/modules', '/usr/share/ansible/plugins/modules']
  ansible python module location = /home/jborean/dev/ansible/lib/ansible
  ansible collection location = /home/jborean/dev:/home/jborean/ansible/collections:/usr/share/ansible/collections
  executable location = /home/jborean/.pyenv/versions/ansible-310/bin/ansible
  python version = 3.10.2 (main, Jan 18 2022, 12:56:09) [GCC 11.2.1 20211203 (Red Hat 11.2.1-7)] (/home/jborean/.pyenv/versions/3.10.2/envs/ansible-310/bin/python3.10)
  jinja version = 3.1.1
  libyaml = True
```


### Configuration

```console
N/A
```


### OS / Environment

N/A

### Steps to Reproduce

```yaml
- command: whoami
  become: '{{ item }}'
  with_items:
  - true
  - false
```

Doing `false` first reversed the problem where the 2nd iteration will not run with become

### Expected Results

First task is run with become and the 2nd is run without.

### Actual Results

```console
Both tasks are run with the first `become` value set.
```


### Code of Conduct

- [X] I agree to follow the Ansible Code of Conduct
return dict(changed=False, failed=True, _ansible_no_log=no_log, exception=to_text(traceback.format_exc()))
        if '_variable_params' in self._task.args:
            variable_params = self._task.args.pop('_variable_params')
            if isinstance(variable_params, dict):
                if C.INJECT_FACTS_AS_VARS:
                    display.warning("Using a variable for a task's 'args' is unsafe in some situations "
                                    "(see https://docs.ansible.com/ansible/devel/reference_appendices/faq.html#argsplat-unsafe)")
                variable_params.update(self._task.args)
                self._task.args = variable_params
        
        no_log = self._task.no_log
        
        
        tempvars = {}
        
        if self._task.delegate_to:
            
            cvars = variables.get('ansible_delegated_vars', {}).get(self._task.delegate_to, {})
        else:
            
            cvars = variables
        templar.available_variables = cvars
        
        if cvars.get('ansible_connection') is not None:
            current_connection = templar.template(cvars['ansible_connection'])
        else:
            current_connection = self._task.connection
        
        if (not self._connection or
                not getattr(self._connection, 'connected', False) or