Q CLI crashes when current working directory is deleted

### 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 26.0.1 (25A362)

### Expected behaviour

When Q CLI deletes its current working directory, it should handle the situation gracefully with one of these approaches:
1. Warn user before deleting the current working directory
2. Prevent deletion of the directory Q is running in
3. Auto-change to parent/home directory after deletion
4. Catch the error and prompt user to change directory instead of crashing

### Actual behaviour

CLI crashes with "No such file or directory (os error 2)" at crates/chat-cli/src/cli/chat/mod.rs:1026

Error output:
Amazon Q is having trouble responding right now:
0: No such file or directory (os error 2)
1: No such file or directory (os error 2)

Location:
crates/chat-cli/src/cli/chat/mod.rs:1026

CLI becomes unresponsive and requires exit. Shell must be reset with cd ~

### Steps to reproduce

1. Start Q CLI in a test directory: `mkdir test-dir && cd test-dir && q`
2. Ask Q to delete the current directory: `rm -rf /full/path/to/test-dir`
3. Send any message after deletion completes
4. CLI crashes with:

Amazon Q is having trouble responding right now:
0: No such file or directory (os error 2)
1: No such file or directory (os error 2)

Location:
crates/chat-cli/src/cli/chat/mod.rs:1026

### Environment

```yaml

[q-details]
version = "1.18.1"
hash = "5610605baef17b76ef41448f2e943f021c2b2273"
date = "2025-10-13T22:31:07.064465Z (11d ago)"

[system-info]
os = "macOS 26.0.1 (25A362)"
chip = "Apple M1 Pro"
total-cores = 8
memory = "16.00 GB"

[environment]
cwd = "/Users/USER"
cli-path = "/Users/USER"
install-method = "brew"

[env-vars]
PATH = "/Users/USER/.local/bin:/Users/USER/.toolbox/bin:/opt/homebrew/bin:/opt/homebrew/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:/Applications/Ghostty.app/Contents/MacOS:/Users/USER/.local/bin"
QTERM_SESSION_ID = "5188b7e3f3cd4a16b7e4c2dd0e7c7a70"
Q_SET_PARENT_CHECK = "1"
Q_TERM = "1.18.1"
SHELL = "/bin/zsh"
TERM = "xterm-ghostty"
__CFBundleIdentifier = "com.mitchellh.ghostty"

[chat-settings]

[chat-trusted_tools]

[chat-failed_request_ids]
none

[chat-context]
current_profile=q_cli_default
profile_context=
AmazonQ.md
AGENTS.md
README.md
.amazonq/rules/**/*.md

files=none
```

Beginne bei crates/chat-cli/src/cli/chat/mod.rs:1026 und reproduziere den Fehler, indem du q in einem Testverzeichnis startest, dieses Verzeichnis löschst und eine weitere Nachricht sendest. Verfolge, wie die CLI nach dem Löschen auf das Arbeitsverzeichnis zugreift, und ermittle ein ordnungsgemäßes Verhalten, das mit den im Issue erwarteten Optionen übereinstimmt. Erledigt ist die Aufgabe, wenn die CLI nicht mehr abstürzt oder nicht mehr reagiert, sobald ihr aktuelles Verzeichnis entfernt wird.

Vom Indexierungsmodell aus dem Issue-Text verfasst.