### 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 (connection_target_node) {
				
				if (!c.callable.is_custom()) {
					ConnectionWithNodePath connection_to;
					connection_to.connection = c;
					connection_to.node_path = p_node->get_path_to(connection_target_node);
					valid_connections_to.push_back(connection_to);
				}
			}
		}
		
		List<Connection> connections_from;
		p_node->get_signals_connected_to_this(&connections_from);
		List<Connection> valid_connections_from;
		for (const Connection &c : connections_from) {
			Node *source_node = Object::cast_to<Node>(c.signal.get_object());
			Node *valid_source_owner = nullptr;
			if (source_node) {
				valid_source_owner = source_node->get_owner();
				while (valid_source_owner) {
					if (valid_source_owner == p_root) {
						break;
					}
					valid_source_owner = valid_source_owner->get_owner();
				}
			}
			if (!source_node || valid_source_owner == nullptr) {
				
				if (!c.callable.is_custom()) {
					valid_connections_from.push_back(c);