Yours

LVP

It’s not the same but it’s close.

Engineered Hardwood

In all honesty, I’d look for engineered hardwood that matches the finish of your hardwood floors. It is less expensive than some of the higher definition LVP, and it’s going to be a better match in the end. Plus, you won’t need a transition from floating flooring to hardwood. I get that you don’t want to break the bank on floors and you might want a lighter look, but consider keeping the same floor throughout. If you ever decide to refinish your hardwood floors to be lighter you can refinish the engineered hardwood as well.

Refinish your floors now. Ciranova Ecofix Plus with the hardener will hold up.

The more unified the flooring, the more unified the home.

The best answer is keep the existing hardwood, add to it, and refinish ALL to whatever tone you like.

The answer won't be to rip all the existing to an LVP.....not as good as what you have.

A rip of ALL the flooring to a much lighter engineered product? That is up to your budget.: )

You should show the framing plan that includes the addition, and all around it.

Some options:

Brick

Mixing tile and hardwood

Unfinished wood stained to match is IMO the best choice and honestly never fake wood next to real . Tile is hard on feet , knees and backs and in a space where you spend a large amount of time never a great idea.

Replacing the flooring with 7-12" wide flat cut European Oak would get you a popular choice. It's a different oak species then N.American oak without the open grain to turn dark.

DuChateau. Lutyens

Monarch Plank

Hurst Hardwoods has product.

You do the flooring if at all possible to be the same wood as you have and the same width of planks