### 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
if not connection:
            raise AnsibleError("the connection plugin '%s' was not found" % conn_type)
        
        if cvars.get('ansible_become') is not None:
            become = boolean(templar.template(cvars['ansible_become']))
        else:
            become = self._task.become
        if become:
            if cvars.get('ansible_become_method'):
                become_plugin = self._get_become(templar.template(cvars['ansible_become_method']))
            else:
                become_plugin = self._get_become(self._task.become_method)
            try:
                connection.set_become_plugin(become_plugin)
            except AttributeError:
                
                pass
            if getattr(connection.become, 'require_tty', False) and not getattr(connection, 'has_tty', False):
                raise AnsibleError(
                    "The '%s' connection does not provide a TTY which is required for the selected "
                    "become plugin: %s." % (conn_type, become_plugin.name)
                )
            
            
            
            self._play_context.set_become_plugin(become_plugin.name)
        
        self._play_context.set_attributes_from_plugin(connection)
        return connection
    def _set_plugin_options(self, plugin_type, variables, templar, task_keys):