### Tested versions

v4.2.stable.official [46dc27791]

### System information

Windows 11- Godot v4.2.stable.official [46dc27791] - Vulkan (Forward+)

### Issue description

When I switch picker mode the next time I open it should be the pick mode I selected last time but it's not

https://github.com/godotengine/godot/assets/46812028/522c8b55-14cf-4781-963f-a465a03c9432



### Steps to reproduce

Toggle a picker mode off and on again

### Minimal reproduction project (MRP)

N/A
Dictionary floating_docks_dump = p_layout->get_value(p_section, "dock_floating", Dictionary());
	bool restore_window_on_load = EDITOR_GET("interface/multi_window/restore_windows_on_load");
	for (int i = 0; i < DOCK_SLOT_MAX; i++) {
		if (!p_layout->has_section_key(p_section, "dock_" + itos(i + 1))) {
			continue;
		}
		Vector<String> names = String(p_layout->get_value(p_section, "dock_" + itos(i + 1))).split(",");
		for (int j = names.size() - 1; j >= 0; j--) {
			String name = names[j];
			
			int atidx = -1;
			Control *node = nullptr;
			for (int k = 0; k < DOCK_SLOT_MAX; k++) {
				if (!dock_slot[k]->has_node(name)) {
					continue;
				}
				node = Object::cast_to<Control>(dock_slot[k]->get_node(name));
				if (!node) {
					continue;
				}
				atidx = k;
				break;
			}
			if (atidx == -1) {
				
				for (WindowWrapper *wrapper : floating_docks) {
					if (wrapper->get_meta("dock_name") == name) {
						if (restore_window_on_load && floating_docks_dump.has(name)) {
							_restore_floating_dock(floating_docks_dump[name], wrapper, i);
						} else {