NATO isn't just the U.S. other members have to agree and it's understandable that European members might be hesitant to expedite Russia's entry when they were fresh off conflicts with Moldova, Georgia, and Ukraine where they were the aggressors.You said it’s a lie that Russia wanted to join NATO but then admitted in the same sentence they wanted to join NATO but through an expedited process. NATOs entire existence was to counteract Russias influence in Europe so why would Russia have to “apply” to join NATO? If the United States really wanted peace like they claim they would have jumped at the opportunity to allow Russia to join.
The United States spent billions supporting pro-western separatists in the Ukraine leading to the 2014 coup. Even far-right neo nazi groups.
If Putin actually cared about joining NATO he would've took the bare minimum steps, but he never intended to join, he was posturing for the public.