Create new or open existing project
Open an asset in that project and click to expand the "Others" section.
Close the asset and go back and open another asset in another project

Open a business process in the other project for example – Project Explorer will have the "Others"
tab expanded again.

I think this should not happen and if Project Explorer must remember the expanded tabs it should be per project only. Better IMO would be to expand the tab for the asset that was actually opened. So for example if .bpmn2 asset was openend File Explorer would expand the "Business Processes" section only.