GTK Inspector can be launched in OS 9 Greeter

### What Happened?

GTK Inspector can be launched if enabled in GSettings in OS 9 Greeter. I couldn't reproduce on latest OS 8 Daily.

### Steps to Reproduce

1. Log in to OS 9 Daily
2. Open Terminal and run `gsettings set org.gtk.gtk4.Settings.Debug enable-inspector-keybinding true`
3. Reboot
4. When Greeter presents, press Ctrl + Shift + I
5. See GTK Inspector appears

### Expected Behavior

GTK Inspector should not be launched as before in OS 8.

### OS Version

Early Access

### OS Architecture

amd64 (on most hardwares)

### Session Type

Secure Session (Wayland, This is the default)

### Software Version

Early Access or Compiled from git

### Log Output

```shell

```

### Hardware Info

_No response_

Reproduce the issue in the OS 9 Greeter using the provided GSettings command and Ctrl+Shift+I shortcut. Then inspect the greeter's GTK Inspector and keybinding handling; done means the inspector no longer launches from the Greeter while the reported setup remains enabled.

Written by the indexing model from the issue text.