### 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)

Z_DEFAULT_COMPRESSION,
					0,
					-MAX_WBITS,
					DEF_MEM_LEVEL,
					Z_DEFAULT_STRATEGY,
					nullptr,
					0,
					0x0314, 
					1 << 11); 
			Ref<FileAccess> fa = FileAccess::open(dir.path_join(f), FileAccess::READ);
			if (fa.is_null()) {
				add_message(EXPORT_MESSAGE_ERROR, TTR("ZIP Creation"), vformat(TTR("Could not open file to read from path \"%s\"."), dir.path_join(f)));
				return;
			}
			const int bufsize = 16384;
			uint8_t buf[bufsize];
			while (true) {
				uint64_t got = fa->get_buffer(buf, bufsize);
				if (got == 0) {
					break;
				}
				zipWriteInFileInZip(p_zip, buf, got);
			}
			zipCloseFileInZip(p_zip);
		}
		f = da->get_next();
	}
	da->list_dir_end();
}
Error EditorExportPlatform::save_pack(const Ref<EditorExportPreset> &p_preset, bool p_debug, const String &p_path, Vector<SharedObject> *p_so_files, bool p_embed, int64_t *r_embedded_start, int64_t *r_embedded_size) {