### Tested versions

Godot Engine v4.2.stable.official.46dc27791

### System information

Windows 10

### Issue description

When exporting to web, Godot fails with this error in the console:

> scene/main/window.cpp:884 - Attempting to make child window exclusive, but the parent window already has another exclusive child. This window: /root/@<!-- -->EditorNode@<!-- -->17120/@<!-- -->Panel@<!-- -->13/@<!-- -->ProjectExportDialog@<!-- -->559/@<!-- -->VBoxContainer@<!-- -->137/@<!-- -->AcceptDialog@<!-- -->411, parent window: /root/@<!-- -->EditorNode@<!-- -->17120/@<!-- -->Panel@<!-- -->13/@<!-- -->ProjectExportDialog@<!-- -->559, current exclusive child window: /root/@<!-- -->EditorNode@<!-- -->17120/@<!-- -->Panel@<!-- -->13/@<!-- -->ProjectExportDialog@<!-- -->559/@<!-- -->ProgressDialog@<!-- -->17444

![a](https://github.com/godotengine/godot/assets/2000051/bf9d22aa-d3fe-4e11-bff6-c387e740fe90)

This happens for newly created empty projects.


### Steps to reproduce

1. Open the attached project (or create a new project).
2. Project->Export->Export All
3. Observe the console error.  No output files are generated.


### Minimal reproduction project (MRP)

[export_test.zip](https://github.com/godotengine/godot/files/13574810/export_test.zip)

"BATTERY_STATS",
	"BIND_ACCESSIBILITY_SERVICE",
	"BIND_APPWIDGET",
	"BIND_DEVICE_ADMIN",
	"BIND_INPUT_METHOD",
	"BIND_NFC_SERVICE",
	"BIND_NOTIFICATION_LISTENER_SERVICE",
	"BIND_PRINT_SERVICE",
	"BIND_REMOTEVIEWS",
	"BIND_TEXT_SERVICE",
	"BIND_VPN_SERVICE",
	"BIND_WALLPAPER",
	"BLUETOOTH",
	"BLUETOOTH_ADMIN",
	"BLUETOOTH_PRIVILEGED",
	"BRICK",
	"BROADCAST_PACKAGE_REMOVED",
	"BROADCAST_SMS",
	"BROADCAST_STICKY",
	"BROADCAST_WAP_PUSH",
	"CALL_PHONE",
	"CALL_PRIVILEGED",
	"CAMERA",
	"CAPTURE_AUDIO_OUTPUT",
	"CAPTURE_SECURE_VIDEO_OUTPUT",
	"CAPTURE_VIDEO_OUTPUT",
	"CHANGE_COMPONENT_ENABLED_STATE",
	"CHANGE_CONFIGURATION",
	"CHANGE_NETWORK_STATE",
	"CHANGE_WIFI_MULTICAST_STATE",