The motivation by Putin has a connection to the Cold Wars Days. After WWII ended, Russia and the Western Allies divided Europe into the East and West, with the Eastern European countries becoming satellites of Russia; Soviet Union. This expansion by Russia, was due to the extreme losses they suffered in WWII, due to the attack by Germany. Russia lost over 25,000,000 people.They vowed never to be unprepared again. They needed and created a buffer zone.
Beginning with Reagan and then Bush #1, the Soviet Union began to decline, as the new technology expanded, and as the many countries in the Soviet Block wanted their independence. This led to the Soviet Union being trimmed down to just Russia. It was now naked and afraid.
There were still many old WWII Russians who were paranoid of this decline; their version of the swamp. They needed reassurances, such as NATO not expanding into their former buffer zone. They got this from Bill Clinton and others, but in the end, this was not carved into stone.
This all changed when Ukraine wanted to be part of NATO. This would have allowed NATO to practice military exercises right at the Russian border. This thought created a lot of internal pressure and paranoia. Putin had to act or risk alienating the Russian swamp. He took over Crimea, as a practice expansion. Obama did not resist, so the next move was planned.
Putin prefers to invade when Democrats control the US government, since they have been allies since the Cold War years. Both liked the idea of socialism; United Soviet Socialist Republic; USSR and US socialism and Big Government.
Biden, who has age related mental problems, provided the perfect cover for the Ukraine invasion. Putin took Crimea under Obama and Biden, with nothing done to him, while allowing him to keep Crimea. He did not invade under Trump. Trump was more like an oligarch cowboy and was not easy to take advantage of. Biden provided a unique opportunity; push over with a history of allowing the expansion.
My guess is if the Republican take over the House and Senate, and Biden becomes more moderate again; former Biden, Putin will try to save face and start peace talks. If the Democrats can steal the election, Putin may decide to expand into the former other satellite countries. Biden will not act, due to not having all his senses, to plan a proper countering move. Biden is also under the control of the extreme left, which has socialism plans. Putin may need to help the Democrats win the midterms or he may have to backtrack and delay again.
Biden should offer Putin reassurance that NATO will not enter former Soviet Satellite countries, but will stay contained, if Putin gets out of Ukraine. This may save face and end the war, while also helping with Russia politics deal with the paranoia of another WWII scale invasion, with no buffer.