As per my post here:
https://community.esri.com/t5/arcgis-pro-questions/selection-layer-does-not-persist-between-projects...
(acknowledged by ESRI staff)...
Currently when you drag and drop or copy and paste a selection layer between instances of ArcGIS Pro it does not honour the selection and instead reverts to showing the whole layer,. This is a change in behaviour from ArcMap and something that would be good to see reintroduced as all other layer properties are retained e.g. symbology/definition queries etc.