The 6-10MT estimate is really a lower bound based on the amount of material moved from the island. A more reliable estimate is based on the overpressure, which was significantly larger than the Tsar Bomba (also exploded over an island) which was 50MT. https://text.npr.org/1074438703
That said, the amount of SO2 was fairly low, so the climate impact not likely to be large.
I heard from an Anton Petrov video it would reduce the planets average temperature by half a degree for some time, but I don't know where he got that info from.
It's possible that estimate was based on the eruption size, not the SO2 amount. It seems that the amount of SO2 emitted wasn't that much, so maybe something much less than 0.5 degF.
We have had really beautiful sunsets here in Northern California for the past week. Maybe related? (We also have a winter wildfire in Big Sur that could be contributing.)
Also whether it will turn the sky red for months.