### 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)

"MANAGE_DOCUMENTS",
	"MANAGE_EXTERNAL_STORAGE",
	"MASTER_CLEAR",
	"MEDIA_CONTENT_CONTROL",
	"MODIFY_AUDIO_SETTINGS",
	"MODIFY_PHONE_STATE",
	"MOUNT_FORMAT_FILESYSTEMS",
	"MOUNT_UNMOUNT_FILESYSTEMS",
	"NFC",
	"PERSISTENT_ACTIVITY",
	"PROCESS_OUTGOING_CALLS",
	"READ_CALENDAR",
	"READ_CALL_LOG",
	"READ_CONTACTS",
	"READ_EXTERNAL_STORAGE",
	"READ_FRAME_BUFFER",
	"READ_HISTORY_BOOKMARKS",
	"READ_INPUT_STATE",
	"READ_LOGS",
	"READ_PHONE_STATE",
	"READ_PROFILE",
	"READ_SMS",
	"READ_SOCIAL_STREAM",
	"READ_SYNC_SETTINGS",
	"READ_SYNC_STATS",
	"READ_USER_DICTIONARY",
	"REBOOT",
	"RECEIVE_BOOT_COMPLETED",
	"RECEIVE_MMS",
	"RECEIVE_SMS",