### 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)

return menu_options;
}
String EditorExportPlatformLinuxBSD::get_option_label(int p_index) const {
	return (p_index) ? TTR("Stop and uninstall") : TTR("Run on remote Linux/BSD system");
}
String EditorExportPlatformLinuxBSD::get_option_tooltip(int p_index) const {
	return (p_index) ? TTR("Stop and uninstall running project from the remote system") : TTR("Run exported project on remote Linux/BSD system");
}
void EditorExportPlatformLinuxBSD::cleanup() {
	if (ssh_pid != 0 && OS::get_singleton()->is_process_running(ssh_pid)) {
		print_line("Terminating connection...");
		OS::get_singleton()->kill(ssh_pid);
		OS::get_singleton()->delay_usec(1000);
	}
	if (!cleanup_commands.is_empty()) {
		print_line("Stopping and deleting previous version...");
		for (const SSHCleanupCommand &cmd : cleanup_commands) {
			if (cmd.wait) {
				ssh_run_on_remote(cmd.host, cmd.port, cmd.ssh_args, cmd.cmd_args);
			} else {
				ssh_run_on_remote_no_wait(cmd.host, cmd.port, cmd.ssh_args, cmd.cmd_args);
			}
		}
	}
	ssh_pid = 0;
	cleanup_commands.clear();
}
Error EditorExportPlatformLinuxBSD::run(const Ref<EditorExportPreset> &p_preset, int p_device, int p_debug_flags) {