Use standard strip oak for the new areas, then sand and refinish everything to match. Formal areas often have ‘fancier’ floors than other parts of the home, color and finish will make it cohesive.

Thank You! You think this is the best option vs rip and replace with all engineered hardwood?

I'm also thinking of using hardwood for kitchen.

Site finished wood has more perceived value than engineered. It will also likely be cheaper. Sure you can rip out the parquet and do engineered throughout, it’s just not the first place i would spend money.

if the parquet is in good shape, you can absolutely have it refinished. I like them.

as for matching it, yes, you can buy more parquet oak tiles in the same species.

It's a beautiful floor when refinished correctly.

some are called 5 finger block oak parquet.

this shows the thinner plank style butting up to it. (prob 2 1/4" or so)

You can easily buy this other flooring and do it. if you do solid, it's stain on site along w/the parquet. (the parquet flooring has to be sanded w/an orbital sander, not a regular forward and back one. So make sure a good pro is hired to do it)

look at how cool it looks in a dark walnut shade w/inlaid regular strips. great for any damaged parts

what you could also do for the parts is a herringbone. (either solid or an engineered)

Emily Hendersen talks about redoing her space w/this oak

https://stylebyemilyhenderson.com/blog/story-herringbone-flooring

If I had the choice, i'd do the herringbone. it's beautiful and completely mcm appropriate
This is a natural finish white oak.

and love the idea in the bathroom to feather in ceramic tiles in the same herringbone

in the kitchen you could do something like this w/some cool cement tiles around the perimeter:

walnut stain color. 5 finger block parquet matches the finger oak herringbone, below:

you could even do the finger oak herringbone to match your parquet (the planks are shorter)

longer sizes.

you could also do a herringbone surrounded by the regular planks.

It will all need to be refinished to at least match and I have no issue with a different flooring on a different level .

I see no reason to coordinate upstairs and downstairs flooring..especially when upstairs is older and will be unlikely to match,anyway...depending on the situation...matching the colors may one way to add continuity...