It might be worth having the tile professionally stripped, cleaned and sealed to see it if changes appearance enough for you to like it. It does look harder to maintain than the clean and shiny look of smooth tile.

Take a cabinet door or drawer and a sample of your countertop with you, along with an extra wood board if you have one. The door over the fridge is usually rarely used and conveniently small to haul around.

Try Daltile aka American Olean for a wide selection of tile. For example,

https://www.daltile.com/products/stone-look/haddonstone/dawn

No accent tile IMO that will scream dated . Judt a nice 12 x24 porcelain in a color that works with the wood . Those floors look really rustic so what is your style ?

Please post kitchen pics and more pics of foyer and dining living area.

That slate is high end valuable and desirable. Way better and higher quality than the wood. Have it cleaned and sealed, rather than spend 30K+ on new floors.

And, get an electrician in there for better lighting. That really is not a dark floor. It's your lighting that's the issue.

a light colored porcelain tile to lighten the rooms.

https://www.tileshop.com/products/chester-silver-versailles-porcelain-wall-and-floor-tile-680252

Here's an extensive "before and after" stone gallery:

https://www.sirgrout.com/before-and-after-stone/

"Dark" rooms need lighting. Period.