Mainly, why did Putin do it? Because clearly the deal benefits Biden and the Harris campaign and presumably Putin prefers Trump.
1) The key to the deal from Putin's point of view was the KGB assassin held by Germany. Trump's relationship with Scholz is poor, as it is with most European leaders not named Orban. So if Trump is re-elected, Putin may have believed a deal was far less likely.
2) The deal, involving Germany, Slovakia, Romania and Turkey, clearly shows the strength of the NATO alliance. Why would Putin want to strengthen NATO when it's helping Ukraine kick his ass? Perhaps Putin felt his popularity in Russia had tanked and he needed the photo op of him greeting returning prisoners. It's a mystery.

Honestly, I do not think Putin was focusing on how this impacts the election. Even if he was, if he was dealing more with Biden, he may have felt it didn't matter since Biden is out. It would take him seeing how this benefits Harris for there to be any pause. But more likely he is even more focused on how he sees this benefiting him and Russia.

I always got the impression Putin was quite popular in Russia. From everything I could find, his approval was 71% before the Ukraine war and it’s now up to 86%. I couldn’t find anything that refutes this, but I can imagine how people in Russia might not feel comfortable saying they don’t support him.  

This was a very complicated deal, and negotiations probably went sideways several times before all the parties were lined up in agreement. Any concern Putin may have had about helping US Democrats was overridden by the opportunity to get his hit man back on Russian soil. Once the window of opportunity opened, the agreement was sealed.