kiro-cli doctor fails with "Unsupported terminal" inside of 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

macOS 15.7.2 (24G325)

### Expected behaviour

Outside tmux (tmux version 3.6, on both iTerm2 and Terminal), I get:
```
$ kiro-cli doctor

✔ Everything looks good!

Kiro CLI still not working? Run kiro-cli issue to let us know!
```

### Actual behaviour

Inside tmux (tmux version 3.6, on both iTerm2 and Terminal), I get:
```
$ kiro-cli doctor

✘ Terminal support: Unsupported terminal, if you believe this is a mistake or would like to see support for your terminal, run kiro-cli issue

__CFBundleIdentifier: com.raycast.macos

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

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

I don't have any sort of raycast-tmux integration installed that I know of, so I don't know why the `__CFBundleIdentifier` points to raycast.

### Steps to reproduce

It's unclear to me if something environmental needs to be set regarding raycast, but in general the steps are:
1. start tmux session: `tmux new -s test-kiro-cli`
2. run doctor: `kiro-cli doctor`

### Environment

```yaml

[q-details]
version = "1.21.0"
hash = "dc54efd85f411d6b4347d192733ff40650d38dfb"
date = "2025-11-26T22:31:44.946762Z (9d ago)"
variant = "full"

[system-info]
os = "macOS 15.7.2 (24G325)"
chip = "Apple M1 Pro"
total-cores = 10
memory = "32.00 GB"

[environment]
cwd = "/Users/USER"
cli-path = "/Users/USER"
os = "Mac"
shell-path = "/bin/zsh"
shell-version = "5.9"
install-method = "unknown"

[env-vars]
PATH = "/opt/homebrew/bin:/opt/homebrew/sbin:/Users/USER/.bun/bin:/Users/USER/.toolbox/bin:/Users/USER/bin:/Users/USER/.local/bin:/Users/USER/.gitbin:/Users/USER/.rbenv/shims:/Users/USER/sandbox/bin:/Applications/Firefox.app/Contents/MacOS:/opt/homebrew/opt/node@18/bin:/Users/USER/bin/maven/bin:/Users/USER/.asdf/shims:/Users/USER/.asdf/bin:/Users/USER/.nvm/versions/node/v18.20.3/bin:/opt/local/bin:/opt/local/sbin:/usr/local/bin:/System/Cryptexes/App/usr/bin:/usr/bin:/bin:/usr/sbin:/sbin:/var/run/com.apple.security.cryptexd/codex.system/bootstrap/usr/local/bin:/var/run/com.apple.security.cryptexd/codex.system/bootstrap/usr/bin:/var/run/com.apple.security.cryptexd/codex.system/bootstrap/usr/appleinternal/bin:/Library/Apple/usr/bin:/Users/USER/.cargo/bin:/Applications/iTerm.app/Contents/Resources/utilities:/Users/USER/Library/Application Support/JetBrains/Toolbox/scripts"
QTERM_SESSION_ID = "6da3d8818fbf4d88b9f7b80f7dc65ed6"
Q_SET_PARENT_CHECK = "1"
Q_TERM = "1.21.0"
SHELL = "/bin/zsh"
TERM = "tmux-256color"
__CFBundleIdentifier = "com.raycast.macos"
```