Excellent and intriguing ideas, OP, well done! The red and blue colors are obvious ancient color star markers - now that you point them out. One of those "now why didn't I think of that" moments.

Could one effect the other? Probably, through the hyperdimensional torsion fields that connect the stars.

As for a mass transfer, probably not as it is too large a distance, but as ripples and interactions in hyperdimensional fields of energy, absolutely. Also as blasts of hyperdimensional energy in the case of a supernova explosion.

I believe a nova can happen more than once, as successive layers are blown off of the star, because an intact an sometimes fairly large star is left after the nova explosion of the outer shell. But a supernova is so tremendous, I doubt much would be left to form a future nova.

And one more thing - if we are being visited by beings with faster-than-light travel capabilities (or if we secretly developed it ourselves), then "ancient" prophecies could have been seeded into cultures about Betelgeuse exploding because, to those with FTL ships, they already saw it happen. In which case, we're just waiting for the light (and hyperdimensional effects) of the blast to reach us at the speed of light.

And who knows - maybe some hyperdimensional effects are faster than light, and have already reached us, and are having all sorts of effects we don't recognize, coming from a star we don't know has already exploded.