### 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)

CharString cs = import_text.utf8();
				Vector<uint8_t> sarr;
				sarr.resize(cs.size());
				memcpy(sarr.ptrw(), cs.ptr(), sarr.size());
				err = p_func(p_udata, path + ".import", sarr, idx, total, enc_in_filters, enc_ex_filters, key);
				if (err != OK) {
					return err;
				}
				
				sarr = FileAccess::get_file_as_bytes(export_path);
				err = p_func(p_udata, export_path, sarr, idx, total, enc_in_filters, enc_ex_filters, key);
				if (err != OK) {
					return err;
				}
			} else {
				
				Ref<ConfigFile> config;
				config.instantiate();
				err = config->load(path + ".import");
				if (err != OK) {
					ERR_PRINT("Could not parse: '" + path + "', not exported.");
					continue;
				}
				String importer_type = config->get_value("remap", "importer");
				if (importer_type == "keep") {
					
					Vector<uint8_t> array = FileAccess::get_file_as_bytes(path);
					err = p_func(p_udata, path, array, idx, total, enc_in_filters, enc_ex_filters, key);
					if (err != OK) {
						return err;