The states that stopped the additional UE benefits did so somewhere between the middle of June into the few 2 weeks of July, which means it's too soon to know whether or not that decision affected labor participation. But in any case, you lied because there is no data available to compare these states against the others.
However, does it not make sense that after those supplemental benefits expire the people in those states are more likely to go find a job cuz they'll be getting less money than the other states that will continue to pay the extra money? Obviously there are other factors involved, demand is higher in some places vs other, etc. But surely anyone with an ounce of common sense can see that if you pay people enough money NOT to work, then they won't.