### 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)

uint32_t attr_resid = decode_uint32(&p_manifest[iofs + 16]);
					const String value = (attr_value != 0xFFFFFFFF) ? string_table[attr_value] : "Res #" + itos(attr_resid);
					String attrname = string_table[attr_name];
					const String nspace = (attr_nspace != 0xFFFFFFFF) ? string_table[attr_nspace] : "";
					
					if (tname == "manifest" && attrname == "package") {
						string_table.write[attr_value] = get_package_name(package_name);
					}
					if (tname == "manifest" && attrname == "versionCode") {
						encode_uint32(version_code, &p_manifest.write[iofs + 16]);
					}
					if (tname == "manifest" && attrname == "versionName") {
						if (attr_value == 0xFFFFFFFF) {
							WARN_PRINT("Version name in a resource, should be plain text");
						} else {
							string_table.write[attr_value] = version_name;
						}
					}
					if (tname == "application" && attrname == "requestLegacyExternalStorage") {
						encode_uint32(has_read_write_storage_permission ? 0xFFFFFFFF : 0, &p_manifest.write[iofs + 16]);
					}
					if (tname == "application" && attrname == "allowBackup") {
						encode_uint32(backup_allowed, &p_manifest.write[iofs + 16]);
					}
					if (tname == "application" && attrname == "appCategory") {
						encode_uint32(_get_app_category_value(app_category), &p_manifest.write[iofs + 16]);
					}
					if (tname == "application" && attrname == "isGame") {
						encode_uint32(app_category == APP_CATEGORY_GAME, &p_manifest.write[iofs + 16]);
					}