For how long would it be that bright?

Full moon energy concentrated on a small dot that has 100,000x smaller angular area might be able to damage your eye? I don't know, I didn't do the math

The sun is about 400,000x the brightness of the moon, with about the same apparent size. So I think the full moon's brightness concentrated 100,000x would be almost that bad. However, having the sun in your field of view momentarily doesn't blind you (disclaimer: don't stare at the sun until it blinds you; that will blind you ("solar retinopathy")).

There are a couple of other factors. Supernova "light curves" only reach their maximum gradually over several days. Also, your eye doesn't focus an arbitrarily small light source to an arbitrarily small spot on the retina. Instead it's something like an "airy disk". At some point, the relationship between apparent size and the size of the (blurred, "diffraction limited") image on the retina is appreciably non-linear. I think it matters in this case, because Betelgeuse is a lot smaller than the eye's "resolution" of about 1/60th degree. So its light is concentrated that much less (squared). In a supernova, the "size" of the star increases over time, though maybe not enough to matter, even for Betelgeuse.

The small dot would be equivalent in brightness to the full moon, meaning if you looked at both with a luxometer, they would look equally bright. It's not saying that the star will be as bright as the Moon, but concentrated down - that's not how brightness works...