### 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
try:
            plugin = getattr(self._connection, '_%s' % plugin_type)
        except AttributeError:
            
            plugin = getattr(self._connection, plugin_type)
        
        
        if plugin_type == "ssh_type_conn":
            plugin_type = "connection"
        option_vars = C.config.get_plugin_vars(plugin_type, plugin._load_name)
        options = {}
        for k in option_vars:
            if k in variables:
                options[k] = templar.template(variables[k])
        
        plugin.set_options(task_keys=task_keys, var_options=options)
        return option_vars
    def _set_connection_options(self, variables, templar):