"Fig failed to init logger"

### 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 15.7.0 (24G222)

### Expected behaviour

Fig initializes logger without issue.

### Actual behaviour

```shell
Last login: Thu Sep 25 10:11:54 on ttys008
Fig failed to init logger: Io(Os { code: 13, kind: PermissionDenied, message: "Permission denied" })
--------------------------------------------------------------------------------
~ » brigilre@HOSTNAME
```

### Steps to reproduce

1. Open new MacOS Terminal window

### Environment

```yaml

[q-details]
version = "1.16.2"
hash = "ad0c864cba444a41b06b43e119f1d6bbc21bcf06"
date = "2025-09-19T04:23:46.287353Z (7d ago)"
variant = "full"

[system-info]
os = "macOS 15.7.0 (24G222)"
chip = "Intel(R) Core(TM) i7-9750H CPU @ 2.60GHz"
total-cores = 6
memory = "16.00 GB"

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

[env-vars]
PATH = "/Users/USER/.pyenv/shims:/Users/USER/Library/pnpm:/Users/USER/.local/bin:/usr/local/bin:/usr/local/sbin:/Users/USER/.jenv/shims:/Users/USER/.nvm/versions/node/v22.18.0/bin:/Users/USER/.rd/bin:/Library/Frameworks/Python.framework/Versions/3.13/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/.local/bin:/Users/USER/.local/bin"
QTERM_SESSION_ID = "0c4a9f67bdf14a0881a5f395a1219aa9"
Q_SET_PARENT_CHECK = "1"
Q_TERM = "1.16.2"
SHELL = "/bin/zsh"
TERM = "xterm-256color"
__CFBundleIdentifier = "com.apple.Terminal"
```