I'm preparing multiple layouts of the same geographical extent from one Map canvas. The layer which is selected in Map canvas is displayed in every layout. Is it possible to turn off this automatic synchronization in ArcGIS pro 2.9?
This is what is under layout control
Layout and the Contents pane—ArcGIS Pro | Documentation
and this is how a layout behaves
Add and modify map frames—ArcGIS Pro | Documentation
Is this the behaviour you are seeking to supress?
Note:
While the map extent of each map frame is independent of other map frames, the contents of a map frame's map are not. A map frame is just like having another map view open. For example, if you select some features on a map, those features are selected in all open views of that map—including in map frames. Likewise, if you turn off a layer in one view, it turns off in all views. Layer properties cannot be set per view.
There is an idea for what you are requesting: Locked Multiple Layouts in ArcGIS Pro - Esri Community
I'd recommend going there and adding your kudo.