### 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)

"CHANGE_WIFI_STATE",
	"CLEAR_APP_CACHE",
	"CLEAR_APP_USER_DATA",
	"CONTROL_LOCATION_UPDATES",
	"DELETE_CACHE_FILES",
	"DELETE_PACKAGES",
	"DEVICE_POWER",
	"DIAGNOSTIC",
	"DISABLE_KEYGUARD",
	"DUMP",
	"EXPAND_STATUS_BAR",
	"FACTORY_TEST",
	"FLASHLIGHT",
	"FORCE_BACK",
	"GET_ACCOUNTS",
	"GET_PACKAGE_SIZE",
	"GET_TASKS",
	"GET_TOP_ACTIVITY_INFO",
	"GLOBAL_SEARCH",
	"HARDWARE_TEST",
	"INJECT_EVENTS",
	"INSTALL_LOCATION_PROVIDER",
	"INSTALL_PACKAGES",
	"INSTALL_SHORTCUT",
	"INTERNAL_SYSTEM_WINDOW",
	"INTERNET",
	"KILL_BACKGROUND_PROCESSES",
	"LOCATION_HARDWARE",
	"MANAGE_ACCOUNTS",
	"MANAGE_APP_TOKENS",