Here is one more picture.

Looks like a soft pine (white pine or spruce) therefore getting a commercial drum sander to remove the paint is going to remove a lot of material in a hurry. Then applying a finish like polyurethane, which can only be removed by sanding (again) locks you into a cycle wherein your historic material is carted to the landfill as dust in garbage bags. Within a few cycles, the flooring will be abraded down to the t&g, and effectively ruined.
The good new as I see it is that these floors have not been previously sanded, as they apparently been covered with area rugs and a painted border (a very typical treatment in the 19th century).
There's no reason why you couldn't repeat this, and choose your personal floor paint color, and use a Persian (or a modern rug) of an appropriate size. It would look 100% authentic.
There is an issue of which I must make you aware. Those never-painted central patches are never going to match the wood underneath the painted borders if both of them are stripped down. The bare patches have 160 years more oxidation head start, and will be darker when varnished. Artful (painfully so) staining work can diminish the differences a great deal, as will a flat finish, but this is really an art, and a historic floor specialist (or experienced, determined homeowner who's good at wood finishing, or gets ones self to that point) would need to take charge.
We hand scrape old/historic floors where there is high regard for them or they are nearing the point where the t&g will become exposed. Our hand scraping bears no relationship to the current factory process of intentionally putting scraper tracks into material for the sake of added texture. We are scraping to have total control inch by inch over how much material gets removed, where; to keep material removal to the minimum level to render the floorboards smooth and finish-ready. The scraper gives complete control and can leave an even layer of oxidised wood (patina) that a power-sanding would render very much flatter, but with infinitely varying degrees of patina. With a cupped board, fo instance, a sander will sand the cupping completely out, in the process removing less material at the center (low point of the cup) and greatly more material at the edges, rendering two lighter stripes and a darker center. On wide pine boards this is very pronounced.
This is too long, sorry, here is a pic of one of our scraped-process floors, of wide heart pine, where there had been very bad weathered. sun-faded patches in line with the window, and the 14-16" wide boards would not have withstood drum sanding.

Where is the house? That helps ID the floor because it's usually a local wood.

Instead of drum sanding, strip the floor with "soy gel". Non-toxic and non-stinky. Then scuff sand with a square "screening sander" (easier to use than a drum sander and chews off way less wood) and apply several coats of an oil finish like Velvet-Oil or Waterlox and see what it looks like.

We have the same problem - some areas painted, everywhere a milky varnish. We are trying to restore the house authentically and avoid toxic materials. So which would be best for final coat - varnish or shellac or ? Right now we have soaked the old wood with raw linseed oil after sanding where the floors were very bad. We are thinking stain or a linseed oil paint “wash”, then?? NO POLY. Is tung oil harder than linseed oil?