Stars emit neutrinos. Even if we could detect them easily (hard because as you point out they're very weakly interacting, see other answer), neutrino emissions are hardly a "clear channel" where nuclear technology is likely to be the main source of signals.
(Possibly viable if you can filter by neutrino energy, though, but maybe still not.)
Even on earth where our nuclear reactors are much closer than the Sun: (wikipedia)
The majority of neutrinos in the vicinity of the Earth are from nuclear reactions in the Sun. In the vicinity of the Earth, about 65 billion (6.5×1010) solar neutrinos per second pass through every square centimeter perpendicular to the direction of the Sun
To "outshine" our sun, a reactor has to be right next to the detector. (Sorry I don't have quantitative numbers on this).
From another solar system, we'd have the same problem as with visible light: the sun outshines the planets and is very close relative to the distance from them to us. Even a nuclear explosion is peanuts compared to what stars do continuously.
Like a photon or a cosmic ray, a neutrino can have any amount of energy.
Current detection methods have a minimum energy threshold, and can't detect the low-energy neutrinos left over from the Big Bang, or the lower-energy neutrinos from reactors. Wikipedia's main article is pretty short on numbers, and I haven't taken the time to dig further because this idea appears to be so far away from being plausible with current technology.
Supernovae produce very energetic neutrino / antineutrino pairs simply from being so hot (~100 billion Kelvins at the neutron core so there's enough free energy for pair-production).
I'm not sure if anything would distinguish neutrinos produced by fusion in a star from sources like a fission reactor that is more likely to be technological. (Or anti-matter annihilation, if you're looking for Star Trek technology levels.)