How can I record with the presenter's layout?

@NoaCohenOrlov - I am not sure what you mean by "presenter's layout".  If you want to record what the presenter is seeing, the presenter would have to record locally since that always records their view.  If you are thinking you want to record and always have the presenter visible, you should use cloud recording, select "Record Active Speaker and Screen Share", then spotlight the presenter so they are always visible as the active speaker, or just record the "Active Speaker" if you do not want what they are screen sharing.

Presenter's layouts give the presenter new ways of displaying him/herself on top of the shared content. It affects the meeting itself, but not the recording. I want it to display n the chosen layout in the recording as well.

@NoaCohenOrlov - The you (or someone on the meeting) will have to record the meeting locally.  That will capture the meeting exactly as the person recording it sees it on their screen.