humanity, defined loosely, can
definitely build a bigger reactor than the sun. the milky way is a trillion times bigger than the sun, and mostly made up of stars (as opposed to large black holes, which are probably effectively inaccessible), so there's plenty of material available
already-existing natural blue hypergiants can reach energy outputs several million times that of the sun, in large part because they're on the order of 100 times bigger, usually limited only by the eddington mass limit. bat99-98 is estimated at 226 solar masses. so designed artificial stars can clearly reach that size, and conceivably, with a better understanding of plasma dynamics, they could be stabilized. in fact, we already know† how to build an even larger star: if you build a star of very low metallicity (similar to natural population-iii stars, of which possibly none survive today), its eddington mass limit is much higher, around 1000 solar masses
more likely, though, the humans will instead build a larger number of smaller, safer reactors. microscopic black holes can convert mass into hawking radiation at manageable photon energies and useful power levels. the necessary experimentation poses no risk of creating a large black hole (the density of matter necessary to grow small black holes to macroscopic proportion doesn't exist outside of the cores of stars, and the necessary quantity of matter at those densities is also literally astronomical) but will surely involve many explosions as starving black holes explode in a final tantrum of high-energy gamma rays, and of course must be carried out in free fall to prevent your nascent black hole from simply falling between the atoms of your laboratory floor before exploding deep inside your chosen planet
constructing larger reactors, by contrast, does pose a risk of producing phenomena such as disappointing white dwarfs, neutron stars, and black holes, or worse, supernovae, rather than a useful power source
if we believe dyson's calculations, though, a much more worthwhile thing to do is to figure out how to slow down our entropy production enough to preserve life into the cold, dark post-stellar era
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† i mean we know in scientific terms what the structure of such an artificial star would be, where to find the materials, and what would be required to bring them together in the right way. it's fairly simple, actually. the only difficult part is getting a large enough budget to build the necessary fleet of spacecraft to harvest 10³³ kg of hydrogen and helium, about a billionth of the milky way, and bring it together over a distance of several light years; plausibly you need on the order of 10³⁵ spacecraft, about 120 doublings of a von neumann probe