With four months until the November election, the decisions may mean there will be no public revelations about Mr Trump’s financial affairs during an already difficult re-election battle.
I am not sure if the "with" here means at particular points.
Save that, Both decisions pointed towards further litigation in the pair of the cases, with the court sending the subpoenas back to the lower courts for additional proceedings.
The “with” here means meanwhile something happens？
I failed to find an appropriate definition for it in these cases. Source:https://www.ft.com/content/2f249f8c-3aaa-4c41-bbe0-e78fd577b2ab