ssm start-session messes up the terminal after timeout on WSL

### Describe the bug

_Note: this issue was originally opened here: https://github.com/aws/aws-cli/issues/7574, but I was advised to re-open it here._

On WSL the `aws ssm start-session` command corrupts my terminal after it terminates due to inactivity. Regardless of what key I press, no characters appear in the terminal any more. I have tried Ctrl + C too, but it doesn't change the unresponsiveness of my terminal either.

### Expected Behavior

I should be able to use the terminal for other commands.

### Current Behavior

Regardless of what key I press, nothing appears in the terminal. The consequence of this is that I have to close the terminal and open a new one after more-or-less every connection, which is uncomfortable, considering that my history is gone, I have to go back to the same directory and have to initialize my AWS context again.

### Reproduction Steps

1. Install Ubuntu 2020 using WSL 2 on a Windows Enterprise machine.
2. Install AWS CLI and the SSM plugin
3. Launch a session with `aws ssm start-session --target i-XXXXXXXXXXX`
4. Wait 5 minutes
5. Now the terminal becomes unresponsive

### Possible Solution

_No response_

### Additional Information/Context

I start the ssm session like this:
```
aws ssm start-session --target i-0ac4445bb00XXXXXX
Starting session with SessionId: XXXX@YYYY.com
sh-4.2$ id
uid=1001(ssm-user) gid=1007(ssm-user) groups=1007(ssm-user) context=system_u:system_r:unconfined_service_t:s0
```

Then I wait a couple of minutes and press a random key:
```
sh-4.2$ Cannot perform start session: write tcp 172.22.193.94:55404->193.106.225.65:8080: write: broken pipe
```

The session is terminated due to some timeout. The problem occurs _after this_, as my terminal becomes unusable for further commands, nothing appears on my screen any more as I type.

### CLI version used

aws-cli/2.9.12 Python/3.9.11 Linux/5.10.16.3-microsoft-standard-WSL2 exe/x86_64.ubuntu.22 prompt/off

### Environment details (OS name and version, etc.)

Windows 10 Enterprise, WSL 2, Ubuntu 2020