I agree that Putin was sending Trump a message that Trump is Putin's bitch.

As you note, a sex tape has no "legs". Given all of the horrible stuff that is known about Trump, it would have no effect.

Melania hates Trump and his only purpose for her is transactional.

My theory, based on nothing but speculation, is that Putin has Trump on record admitting to a US Federal crime.

We know that Trump got hundreds of millions of dollars of Russian money. Much of this money was the result of illegal transfers. Knowingly accepting the money, knowing its illegal origin would result in a Federal indictment. If they recorded Trump or one of his kids acknowledging that the money was illegal, Trump would be in trouble. This would be something he would want to cover up.

Of course my guess is that Trump now believes, with some reason, that he is immune to any criminal prosecution. He can't be prosecuted while he's president. If he is charged after he leaves office his experience is that he can slow down the case so dies of old age before he goes to trial.