A fully-mortised automatic door bottom will drop when the door is closed, sealing against light and a bit of sound.

Personally, I'd cut, screw and glue a piece of stained wood to one of the doors and see how it looked. Imperfections on a century home often just blend in.

Well, who knew? youtube is so smart...I wonder who its parents were? : > }

I would think you add wood to the bottom of the door, yes? No. It is all about the trim. Skip the ads. Even I could understand it and that is saying a lot.

https://www.youtube.com/watch?v=PgP4pJDBUlE

The OP makes no reference to gaps between the baseboard and flooring. In that case, it's simplest to extend the door. Duh!

Otherwise, pricing out the cost of a trim carpenter, repairs to plaster--no drywall in century homes--and new baseboards and trim might lead you back to a simpler approach. Duh!

I think a good finish carpenter can add apieceon the bottom and refinish the whole door to match.

a 100-year old door is likely cope-and-stick construction with vertical stiles and a bottom rail between them. I'm less optimistic adding a single piece at the bottom will look good, but it's worth doing the experiment to find out.

Tell yourself you will address it in twelve months. If you still even notice at that point feel free to add wood to the bottom.