Cann't run in tmux

### Checks

- [X] I have searched [github.com/aws/amazon-q-developer-cli/issues](https://github.com/aws/amazon-q-developer-cli/issues?q=) and there are no duplicates of my issue
- [X] I have run `q doctor` in the affected terminal session
- [X] I have run `q restart` and replicated the issue again

### Operating system

Linux 5.10.230-202.885.amzn2int.x86_64 - Amazon Linux 2

### Expected behaviour

Amazon Q Cli completions should run as normal in tmux session.

### Actual behaviour

Not run and `q doctor` reports errors

```
❯ q doctor

✘ Qterm Socket Check: Socket exists but could not connect: Connection refused (os error 111)

✘ Doctor found errors. Please fix them and try again.

If you are not sure how to fix it, please open an issue with q issue to let us know!
```

### Steps to reproduce

1. Install Amazon Q locally.
2. Enable ssh integration.
3. Amazon Q runs successfully on remote.
4. Execute `tmux` on remote to open an session.
5. Use as normal

### Environment

```yaml
[q-details]
version = "1.6.0"
hash = "6d13844d6546a5c29e7e121450af1130eb189e7f"
date = "2025-01-09T00:46:48.09362Z (2d ago)"
variant = "minimal"

[system-info]
chip = "AMD EPYC 9R14"
total-cores = 64
memory = "246.40 GB"

[system-info.os.linux]
kernel_version = "5.10.230-202.885.amzn2int.x86_64"
id = "amzn"
name = "Amazon Linux"
pretty_name = "Amazon Linux 2"
version_id = "2"
version = "2"
variant = "internal"

[environment]
cwd = "/local/home/USER"
cli-path = "/local/home/USER"
os = "Linux"
shell-path = "/local/home/USER/.toolbox/tools/toolbox/1.1.1651.0/toolbox-exec"
shell-version = "5.8"
install-method = "toolbox"
in-ssh = true

[env-vars]
PATH = "/home/USER/.local/share/mise/installs/node/18.20.2/bin:/home/USER/.local/share/mise/installs/python/3.12.7/bin:/home/USER/.local/share/mise/installs/python/3.11.10/bin:/home/USER/.local/share/mise/installs/python/3.10.15/bin:/home/USER/.local/share/mise/installs/python/3.9.20/bin:/home/USER/.local/share/mise/installs/python/3.8.20/bin:/home/USER/.local/share/mise/installs/ruby/2.7.8/bin:/home/USER/.toolbox/bin:/usr/lib/jvm/java-17-amazon-corretto.x86_64/bin:/home/USER/.toolbox/bin:/usr/lib/jvm/java-17-amazon-corretto.x86_64/bin:/home/USER/.cargo/bin:/usr/local/bin:/usr/bin:/home/USER/bin:/usr/local/sbin:/usr/sbin:/home/USER/.local/bin:/home/USER/bin:/apollo/env/envImprovement/bin:/apollo/env/AmazonAwsCli/bin/:/home/USER/bin:/apollo/env/envImprovement/bin:/apollo/env/AmazonAwsCli/bin/"
QTERM_SESSION_ID = "4219d93f89bd4b9d963b4f09861e11f5"
Q_PARENT = "/tmp/q-parent-92e543f5b978
```