### 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
if (bottom_panel_updating) {
		return;
	}
	ERR_FAIL_INDEX(p_idx, bottom_panel_items.size());
	if (bottom_panel_items[p_idx].control->is_visible() == p_enable) {
		return;
	}
	if (p_enable) {
		bottom_panel_updating = true;
		for (int i = 0; i < bottom_panel_items.size(); i++) {
			bottom_panel_items[i].button->set_pressed(i == p_idx);
			bottom_panel_items[i].control->set_visible(i == p_idx);
		}
		if (EditorDebuggerNode::get_singleton() == bottom_panel_items[p_idx].control) {