None of what follows is Canon.
I'm not aware of a source in either Canon or Legends, but real actual physicists from the University of Leicester wrote a paper calculating the energy requirements of the Death Star, appropriately titled "That's no Moon". Using a simplified model of an Earth-like planet, they calculate the gravitational binding energy. From the abstract:
A simplified planet is used giving an energy required to destroy it as 2 x 1027 J[oules]J[oules].
But the question asked for Watts, which is just Joules over time. The scene from A New Hope is on YouTube. By my count, the complete beam is sustained for three seconds. According to my hyper-accurate mathAccording to my hyper-accurate math, this puts the Death Star's power output at approximately 6.67 x 1026 WattsWatts, at minimum.
Going back to actual physicists, the "That's No Moon" paper makes some claims about the Death Star's power output, citing the 2007 novel Death StarDeath Star:
[T]he death star [sic] had a very large 'hypermatter' reactor, which possessed an output equal to that of several main-sequence starsmain-sequence stars.
Our sunOur sun is an example of a main sequence star, and it has an estimated energy output (luminosityluminosity) of 3.846 x 1026 Watts.
