### 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)

_process_launcher_icons(file, main_image, launcher_icons[i].dimensions, data);
					}
				}
				if (foreground.is_valid() && !foreground->is_empty()) {
					if (file == launcher_adaptive_icon_foregrounds[i].export_path) {
						_process_launcher_icons(file, foreground, launcher_adaptive_icon_foregrounds[i].dimensions, data);
					}
				}
				if (background.is_valid() && !background->is_empty()) {
					if (file == launcher_adaptive_icon_backgrounds[i].export_path) {
						_process_launcher_icons(file, background, launcher_adaptive_icon_backgrounds[i].dimensions, data);
					}
				}
			}
		}
		if (file.ends_with(".so")) {
			bool enabled = false;
			for (int i = 0; i < enabled_abis.size(); ++i) {
				if (file.begins_with("lib/" + enabled_abis[i].abi + "/")) {
					invalid_abis.erase(enabled_abis[i]);
					enabled = true;
					break;
				}
			}
			if (!enabled) {
				skip = true;
			}
		}
		if (file.begins_with("META-INF") && should_sign) {
			skip = true;