Comment by Sharlin

Not that diffuse; the objects in question are so far away that they're not resolved by JWST. They look like point sources, no matter whether galaxy-sized or vastly smaller (the hypothetical DS objects would "only" be solar-system sized). DM self-annihilation would be rare enough (both due to low DM density and tiny reaction cross-section) that it wouldn't burn out very quickly. The heat (and thus pressure) generated by the annihilation would indeed keep the DSs from collapsing into "real" stars.