Flooring details: Our recently purchased home has mixed-width reclaimed antique granary oak floors - original face/hit-skip. They were finished in a satin oil-based polyurethane and are 3/4" thick.

Problems:
1. The original homeowners did not keep up with maintenance of the floors, and they had never been recoated since their install in 2005. There were spots where the finish had worn off and the wood is greyed out in those spots (wear and tear, dirt, and water damage).
2. We had a large flooring company screen & coat the floors with 2 coats of satin oil-based polyurethane, which improved things somewhat. However, there are some areas where the finish is pulling away from the wood. My guess is this is due to adhesion issues in some areas and/or too thick or improper application on areas where planks are uneven.
3. We would like to extend the flooring on either side of our wood entry, but are worried that the "new" floors won't blend in well with the "old," especially since the mill who milled our original floors went out of business, and the original floors were not maintained.

Question: Can we have as closely matched as possible flooring installed in the rest of the home and refinish it all for a uniform appearance?

I have been told by the bigger installation companies that we cannot refinish the original floor b/c we would lose all of the character and the colors would be stripped (even though our floors were not stained, they just naturally have variations in color ranging from honey to deep espresso). Is this true? I know we would lose some texture, but we are trying to figure out how much texture and color we would lose.

Thank you,
Homeowner who is trying to educate himself on unique flooring

Of course sanding and refinishing will smooth the surface. You can have the refinishing done with a wire brush which will help to texture the surface. It takes an extra step after the surface has been sanded.
If you want a more uniform color, then the floor can be stained.

Thank you. If we decide we don't want to refinish the floors, is there anything that can be done with the random spots where finish is pulling away from the wood?

The spots where the finish is pulling away is caused by poor adhesion. To get better adhesion you will need to get to bare wood. The area can be scraped with a sharp scraper to get the loose finish off, hand sanded with 80 grit paper. then you will need to finish the area to match the surrounding area. Once you get the right color, either by staining or applying a coat of finish, if it is a "natural" color, you will need to slightly abrade the surface and apply another coat, or coats of finish with the matching sheen.
Usually these areas look like a sore thumb and stand out, but with time( and some attractive art on the wall), you will be able to appreciate the floor finish.
Once the floor looks good in these spots, you can apply a final coat of finish over the entire floor. A satin or matte finish will lessen the reflection and help the surface look more even.
It takes time.

Thank you, Pete A. No easy answer it seems, but I appreciate having a better understanding of my options and pros/cons associated with each.