Oh, no, nothing empirical! Musk, the "free speech absolutist" is actually very closed-mouth about actual numbers. Loves to tout metrics that no one can validate, but will not, under any circumstance that I've seen, let anyone do any real research on the metrics. It's all just hearsay based on wire monitoring and patchwork investigations.

The best estimate I've heard is that around 20-30k people really left, based on reported numbers over half a million. That seems about right, to me. 500k said they were going to leave, only 20k actually did.

Of course, why that pushed the site more rightward is likewise speculation. If those numbers are accurate, I'd guess that the people who did leave were the most politically or socially aggrieved, so they would be the exact people to have outsized impact on Community Notes. And given the actual impacts that I've observed, anecdotally, that tracks pretty well with how much further right Twitter got. Not "much" but noticeable to anyone not making excuses for it.