> As he was then constitutionally limited to two consecutive terms as president, Putin served as prime minister again from 2008 to 2012 under Dmitry Medvedev, and returned to the presidency in 2012 in an election marred by allegations of fraud and protests; he was reelected again in 2018. In April 2021, following a referendum, he signed into law constitutional amendments including one that would allow him to run for reelection twice more, potentially extending his presidency to 2036.
Well, some people say that under Medvedev Russia was a bit friendlier with USA:
https://en.wikipedia.org/wiki/Russian_reset
I'm not sure that points highlighted in that article would happen if Putin was president (allowing U.S. forces fly over Russia, supporting Iran sanctions, reducing nuclear arsenals, U.S. dropping plan to build a missile defence shield in Eastern Europe).
The other stuff - seems just like Putin thought "well let them think Russia has changed".