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The problem seems to be that the resultant supernova remnant is going to be very close to the border between black holes and neutron stars. Which one it becomes depends on the original mass of the star, which we don't have accurate measurements for because Betelgeuse is a solo star, not a binary. We have to guess its mass, based on how bright it is, and therefore the mass estimates are tied to the distance estimates - which also have a high degree of uncertainty; it's somewhere between 613 LY and 881 LY away.
Using the lastest guesstimates of distance, mass and rotation rate, the current theory is that when it does go supernova, Betelgeuse will form a 1.5 solar-mass neutron star.
I should also point out that in ED, Betelgeuse is a lot closer than that; it's only 497 LY away. They have presumably used older data that said Betelgeuse was "about 500 LY away". If Betelgeuse actually were that close, then the probability of it forming a neutron star rather than a black hole increases dramatically, as our mass-estimate would drop.
It won't become a second sun. At best it will be like 100x brighter than a full moon with the sun being like a million times brighter.
The "Betelgeuse will be so bright when it explodes it will look like a second sun and or will light up the night as if it's the middle of the day" stories fall into the same category as the old be still recurring made up stories such as "Mars on it closest approach to Earth will make it appear as large if not larger than the moon in the night sky".