Are the multiple Mr. Atoz's possible time aberrations of the same man, and not just clones/holographic duplicates/etc.? It is a time traveling society with the Library seemingly a protected zone against time changes, so why not? This was never really explained in the episode.
It seems that Beta Niobe is a super massive star going into its supernova phase. Kirk's log says that there is only one satellite in the system, planet Sarpeidon, so, in doesn't appear to be a binary star system feeding one star into a Type 1a nova unless he neglected to mention its companion star or his focus of discussion was only on the one planet in the system and then only because they detected that the planet's population disappeared.

The Enterprise is a very busy and in demand ship, so I assume that it would not be assigned to a long term scientific mission to study the nova process. Maybe they were assigned to peek in at the very end, then only to discover the mystery of the sudden population disappearance on Sarpeidon.
Today, the final stage is the most interesting and least scientifically understood. Apparently, a probe or long-range scan of the system detected the supernova process starting (once the star burns off its hydrogen and helium, and starts to burn carbon and oxygen, the process accelerates into eventual core collapse). Knowing the exact mass and composition of the star, the durations of each fuel burn cycles, hence by the 23rd century, Starfleet can predict the supernova explosion to the minute. Nice.
(Reality note: We have identified all the hypergiant and supergiant star candidates for supernova in our corner of the galaxy, and only two within 4000 lys have a chance to explode anytime soon, with "soon" within the next 100,000 years.
Scientific American reports that astronomers have identified the best candidate yet for our galaxy's next supernova explosion, according to a new report. If restricting the exploration limit in the 1000 ly range, then none are predicted to explode over the next 300 years.

Findings published in the February 1 issue of the
Astrophysical Journal suggest that Rho Cassiopeia, located 10,000 light-years away from earth, is most likely to run out of fuel and meet a violent fate in the near future. Other reports that Eta Carinae (which is also in a binary star system) is about 7,500 lys from Earth, in the very last stages of its life, could literally go supernova at any second. But these may also live hundreds, thousands, or even
tens of thousands more years before it does so.)
Based on real science, Beta Niobe is probably a white dwarf star in binary star getting ready to explode due to accumulation of mass from its smaller companion (Alpha Niobe?

). These type supernova (Type 1a) are harder to detect beyond 50-100 lys. Makes more sense.