I think offhand Alpha Centauri miht appear a bright as Venus in the night sky, though I'm not sure about that. It will be like another planet to the ancients, except one that does not move - much.
I think history would not be affected much, though certain Greek myths might be altered to give centaurs a greater prominence.
OK, let´s consider it.
If Toliman is 16 times closer than in OTL, then it is about 6 magnitudes brighter. -6 for Toliman A is plainly and unmistakably brighter than any star or planet - Sirius is -1,43, Venus is -4,3 at brightest. It is not, however, close to Moon: full moon is -12,7.
The distance? The maximum physical distance, 36 au, would at 15 000 au, span 8 arc minutes. One quarter of the diameter of Moon´s disc. Clear to resolve, and B which is only 3,5 times (1,4 magnitudes) dimmer than A would not be lost in glare either. I am not quite sure what the inclination of orbit is, though.
Regarding the speed: if it is orbiting, its speed would be in the region of 400 m/s and period close to 1 million years.
That means a degree in 3000 years - similar to the proper motion of fixed stars.
If, however, Toliman is freely passing Sun by, near its OTL relative speed of 40 km/s, then the proper motion would be in the region of a degree in 30 years. Plainly visible over a lightyear. Over historic period of a few millennia, it would cover most of the sky, change its luminosity and inclination...