q doctor return error message that qterm is not running on VSCode terminal

### 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 6.8.0-1024-aws - Ubuntu 24.04.2 LTS

### Expected behaviour

I'm able to see `q doctor` success without any error messages after all installation process of Amazon Q for command line in my remote Linux instance:

* Started installing the `q` command following [this doc](https://docs.aws.amazon.com/amazonq/latest/qdeveloper-ug/command-line-installing.html)
* At step 4, as the remote instance doesn't have desktop environment, I followed the steps navigated by `q doctor`.
* ran `q integrations install dotfiles`
* add a couple of `sshd_config`
* restarted the machine and reconnected with SSH

### Actual behaviour

I got the following after reconnecting to the remote machine

```
$ q doctor

✘ Amazon Q terminal integrations: qterm is not running in this terminal, please try restarting your terminal

Q_TERM=

✘ 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

Just I followed the steps "Expected behavior".

### Environment

```yaml
[q-details]
version = "1.7.0"
hash = "8885a6708f2f07d02d29460a96f9c422da095e49"
date = "2025-03-06T01:07:14.925938Z (5d ago)"
variant = "full"

[system-info]
chip = "Intel(R) Xeon(R) CPU E5-2686 v4 @ 2.30GHz"
total-cores = 2
memory = "3.82 GB"

[system-info.os.linux]
kernel_version = "6.8.0-1024-aws"
id = "ubuntu"
name = "Ubuntu"
pretty_name = "Ubuntu 24.04.2 LTS"
version_id = "24.04"
version = "24.04.2 LTS (Noble Numbat)"

[environment]
cwd = "/home/USER/repos/zenn.dev.draft"
cli-path = "/home/USER/repos/zenn.dev.draft"
os = "Linux"
shell-path = "/usr/bin/zsh"
shell-version = "5.9"
terminal = "VSCode"
install-method = "unknown"
in-ssh = true

[env-vars]
PATH = "/home/USER/bin:/home/USER/.nodenv/shims:/home/USER/.nodenv/shims:/home/USER/.nodenv/bin:/home/USER/.nodenv/plugins/node-build/bin:/bin:/home/USER/go/bin:/home/USER/bin:/home/USER/.nodenv/shims:/home/USER/.nodenv/shims:/home/USER/.nodenv/bin:/home/USER/.nodenv/plugins/node-build/bin:/bin:/home/USER/go/bin:/home/USER/.vscode-server/cli/servers/Stable-6609ac3d66f4eade5cf376d1cb76f13985724bcb/server/bin/remote-cli:/home/USER/bin:/home/USER/.nodenv/shims:/home/USER/.nodenv/shims:/home/USER/.nodenv/bin:/home/USER/.nodenv/plugins/node-build/bin:/bin:/home/USER/go/bin:/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin:/usr/games:/usr/local/games:/snap/bin:/home/USER/.local/bin:/Applications/Visual Studio Code.app/Contents/Resources/app/bin:/home/USER/.toolbox/bin:/Applications/Visual Studio Code.app/Contents/Resources/app/bin:/home/USER/.toolbox/bin:/Applications/Visual Studio Code.app/Contents/Resources/app/bin:/home/USER/.toolbox/bin"
QTERM_SESSION_ID = "ceb039b7e40e4fb78f6864312e96ec68"
Q_SET_PARENT_CHECK = "1"
Q_TERM = "1.7.0"
SHELL = "/usr/bin/zsh"
TERM = "xterm-256color"
XDG_SESSION_TYPE = "tty"
ZDOTDIR = "/home/USER"
```

Inizia riproducendo `q doctor` in un terminale VSCode all’interno di una sessione SSH remota su Ubuntu 24.04, dopo aver eseguito `q integrations install dotfiles` e `q restart`. Traccia la diagnostica dell’integrazione del terminale che segnala che qterm non è in esecuzione, utilizzando le variabili d’ambiente `Q_TERM`, `QTERM_SESSION_ID` e `Q_SET_PARENT_CHECK` riportate. Il lavoro è completato quando la diagnostica riflette accuratamente lo stato di qterm nei terminali VSCode e dispone di copertura di regressione.

Scritto dal modello di indicizzazione a partire dal testo della issue.