I don't think Biden was being shortsighted about Ukraine. All the Presidents before him took the same calculated risk. They encroached on Russia's borders from all sides in Europe and were hoping that If Ukraine joins Nato too they would take control of the Port in Crimea which would close in the Russia fleet from access to a warm water port.
They calculated that as Russia did not put up a fight to block the rest of the Soviet States from joining Russia, so they must feel weak and unable to take Nato on. When you only listen to advisers which think like you and ignore advice from others who do not, this is the mess you get into.
But never the less it served a useful exercise for the Americans. They were able to sell the Ukrainians all their obsolete armaments although the poor Ukrainians were led to believe that this was aid when sooner or later the price was going to be declared. They have also established the strength of the Russian military and not a single American has been killed in the process. Now that is a good strategy on the part of the Americans.