...Yes, Vermont's daily case counts have "soared" compared to the period of mid-May to early August--from about 0 to 20 daily cases to 339 on October 16. Percentage-wise, it's a colossal increase. Aggregate-number-wise, it's a small number (not to downplay anyone's illness).
The population of Vermont is around 625,000. If 10% are unvaccinated that's about 62,500. If 300 people contract COVID out of that group (Vermont health authorities have been saying that most of the new cases are among the unvaccinated), then 0.5% of this subgroup is showing up each day, on average at this peak, with an infection. I don't see how this shows that vaccination isn't particularly effective at stopping the spread of COVID. If we assumed, in a hypothetical scenario, that 100% of the population of Vermont was unvaccinated and that the rate of 0.5% per day at peak held, that would be more like 3,000 new infections per day--not 300.
Now, setting my hypothetical aside, the paper you reference does say, I would hope, that the increases in COVID are related to the appearance of a new, more infectious variant; and of course, saying that vaccination hasn't reduced case counts ignores the very real possibility that the case counts under Delta would be higher without vaccines.
The key is to define what you mean by "lower case counts haven't played out." It's one thing to mean, lower than we saw before; but it's something else again to mean, lower than would be the case without the vaccines. I think you're saying the latter based on the evidence of the former, which is kind of an apples and oranges thing, especially due to the new variant coming along.
I'm thinking of the system of levees along the Mississippi River in Illinois. Someone could say, gee, it still floods, so what good are those levees? Well, without them, a lot of that land might be permanently inundated.