I would not agree. Every metric is subject to Goodhart's law, approval ratings is no exception. Putin has (allegedly) maintained an approval rating well over 50% for his entire career.
I'm not saying he wants to do right by his constituents, I'm saying he wants to be told he's a winner. Trump is a narcissist. He's all the other terrible things because at the end of the day he needs to feel liked. He will only do things that he thinks will fill that void.