### 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)

if (p_so_func) {
					for (int j = 0; j < export_plugins[i]->shared_objects.size(); j++) {
						err = p_so_func(p_udata, export_plugins[i]->shared_objects[j]);
						if (err != OK) {
							return err;
						}
					}
				}
				for (int j = 0; j < export_plugins[i]->extra_files.size(); j++) {
					err = p_func(p_udata, export_plugins[i]->extra_files[j].path, export_plugins[i]->extra_files[j].data, idx, total, enc_in_filters, enc_ex_filters, key);
					if (err != OK) {
						return err;
					}
					if (export_plugins[i]->extra_files[j].remap) {
						do_export = false; 
						path_remaps.push_back(path);
						path_remaps.push_back(export_plugins[i]->extra_files[j].path);
					}
				}
				if (export_plugins[i]->skipped) {
					do_export = false;
				}
				export_plugins.write[i]->_clear();
				if (!do_export) {
					break; 
				}
			}
			
			if (do_export) {