Thanks for the question.
There are published intentions that the Holy Father has for each month, which the whole Church can pray for. These are usually not controversial.
I understand many feel a hesitancy about praying for anything that Pope Francis has on his personal agenda, because much of it seems to be at odds with our Catholic faith, i.e., the green agenda, sustainable development, etc.
So, this is the essential deal: God would never fulfill any prayer that is against His Will, nor would He allow our sincere prayers to be wasted. So even if you were to pray for the Intentions of the Holy Father, meaning anything and everything that Pope Francis wants, God would sift through that and apply the prayer to the things that were according to His Will.
I pray for the Pope, and the official intentions, everyday when I offer my Rosary. I completely get the disconnect you are probably experiencing, but I trust God above all things. So don't worry and just let your good prayers go to the Poor Souls who need our help, especially at this time.