bug: Autocomplete Feature Not Working in iTerm2 (Quake Mode)

### 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 15.3 (24D60)

### Expected behaviour

The autocomplete feature should work as intended, displaying the autocomplete context menu with suggestions based on the current input.

### Actual behaviour

The autocomplete feature stops working, and the autocomplete context menu is not displayed. This issue seems to be related to how window focus is managed in Quake mode.

### Steps to reproduce

- Open iTerm2
- Configure a profile with the settings shown in the attached screenshots
- Ensure Quake mode is enabled
- Try to use the autocomplete feature of Fig/Q
- Quit iTerm2
- Open iTerm2 by pressing ⌘I
- Type `cd ` (no directories are displayed)

### Environment

```yaml
[q-details]
version = "1.6.0"
hash = "6d13844d6546a5c29e7e121450af1130eb189e7f"
date = "2025-01-09T00:47:39.704258Z (24d ago)"
variant = "full"

[system-info]
os = "macOS 15.3.0 (24D60)"
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"
terminal = "iTerm 2"
install-method = "unknown"

[env-vars]
PATH = "/Users/USER/.krew/bin:/Users/USER/bin/node/bin:/opt/homebrew/opt/coreutils/libexec/gnubin:/opt/homebrew/bin:/opt/homebrew/sbin:/Users/USER/bin:/usr/local/opt/python/libexec/bin:/usr/local/Cellar/vim:/usr/local/opt/inetutils/libexec/gnubin:/usr/local/bin:/usr/local/sbin:/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/Privileges.app/Contents/MacOS:/Applications/Wireshark.app/Contents/MacOS:/Applications/VMware Fusion.app/Contents/Public:/Applications/iTerm.app/Contents/Resources/utilities:/Users/USER/.local/bin:/opt/homebrew/opt/fzf/bin:/Users/USER/go/bin"
QTERM_SESSION_ID = "f27b453255804550afeecb088f46a26f"
Q_SET_PARENT_CHECK = "1"
Q_TERM = "1.6.0"
SHELL = "/bin/zsh"
TERM = "xterm-256color"
__CFBundleIdentifier = "com.googlecode.iterm2"
```

Reproduce the failure in iTerm2 Quake mode on macOS with the reported q 1.6.0 environment, using the documented q doctor and q restart checks. Trace the autocomplete behavior around window focus management; the work is done when typing `cd ` reliably displays directory suggestions after reopening iTerm2 with ⌘I.

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