How to display authorization and registration errors in sessions in bitrix?

Question

1C-Bitrix

I display 2 components on one page (authorization and registration). I would like messages about incorrect password or email to be displayed regardless of the component in any part of the page. Usually such messages are entered into the session, but in Bitrix they are not added to the session. Is it possible to put error output using sessions in the settings somewhere? If not, then tell me how to add it to the session itself, but not in the component template, but in the controller. I think for this then you will need to override component.php in your local folder.