I highly doubt anyone in the US was failing to file a disability claim on Feb 1, 2020. Many things didn't truly start to slow down until the 3rd-4th week of March. And the next data point after that is 29.8k, so let's go with that one. And then you also picked a relative low point in 2010, when 2008 (the beginning of data collection for the graph) or 2012, would have created a lower slope yet again. As a reminder, even if we grant every single one of your curve-fitting maneuvers, we still have absurd significance: 250% increases, which start not at the onset of COVID, but over a year later.
Let's notice the other logical fallacies like assuming the hypothesis and circular reasoning. If you asked reasonable, neutral parties what evidence they would want to see to give credence to the idea that the vaccine is correlated with disability rise, two very specific windows that perfectly correlate mass vaccination with huge rises in disability claims would be the smoking gun. Especially when it also corroborates the anecdotal evidence. It's hard to argue with a hypothesis like yours when it's virtually unfalsifiable.