Yep. I'm with Ihutch13. I can see a bit of wood flooring in a doorway. That would normally rule out any "wood look" tile. The faux sitting beside the real wood makes BOTH look cheap. I recommend a "travertine look" porcelain tile. It is striated (striped) like wood, but it is NOT wood. It comes in DOZENS of different colours. It is a "stone look" type of product that is stunningly beautiful. This would be my recommendation for your situation. Google "travertine porcelain" tiles. You will come up with HUNDRED OF THOUSANDS of photos. They are REALLY stunning. A natural cream coloured travertine (or a tumbled limestone would also work) looking tile would be a great option without worrying about wood-vs-faux wood in your home.

Tile is fashion. Tens of thousands of new choices are discontinued every year and 10,000 new ones are introduced every year. You’re not finding a Alfred Dunner plaid skirt from 1999’s collection, even at TJ Max. You might find it at Goodwill, if you had a network that connected all of the Goodwill’s in the country, and they cataloged their donations to a database. That no more exists than does a database of old discontinued tile. You can’t find replacement tiles for tiles discontinued in 2018, much less 2000. Not unless it was widely used by a tract builder, in a tract neighborhood, and every house comes with a box in the attic. It’s the worse kind of needle in the haystack. Because the haystack is 20 years old. Everything done in 2000 is now 20 years old. Time to assess what has stood that test of time, and what wasn’t a durable or attractive option, and needs to be redone with something else.

Since your wood floor appears to be factory finished or engineered hardwood, it will be INTENSELY difficult to match it. If you can...great but don't set your hopes on it. For that reason I vote "no" to continuing the wood. Not because it would look 'bad' but because it will be near impossible to find. Now onto the question at hand. You have counters that 'read' gray (regardless of the other colours found in them...from 10ft away they look gray = reads gray). You have backslpash that reads gray. You have what appear to be (photos can be deceiving) off-white cabs and a light tan colour on the walls. In other words you have a monochromatic scheme in the kitchen. That makes this a bit more difficult to deal with. Your hardwoods are a deep espresso colour (which mean you have a dark house). This would be easier if the wood was lighter...but that probably won't change for another 10 years....so we have to deal with things as they are. Personally I would say a 'vein cut' travertine-look porcelain tile will look very good in the kitchen. BUT any colour you add to the kitchen (gray with some gray and some off white) is going to have issues with the DARK reddish/brown hardwood. That's where things will need work. Personally I think the ideal colour is currently on your kitchen floor. It is light, it is bright and it is soft enough to work with the wood. An update at this point would be a repeat of what you have. Or you have to choose a THIRD colour for your kitchen. Right now you don't have a third colour. You have monochromatic. A blue slate-look tile would work but your kitchen will look VERY dark...as in 'black hole' dark. A dark(er) floor will require a lighting update, a paint up date and then furniture update. Dark wood table on dark flooring is a tough look to 'like'. That would mean you either update the stools and table OR you find a WHITE or very light AREA RUG to help define the table from the floor (this is super helpful when walking through late at night with the lights off...your toes will thank you for it). Think this through. And think through the hardwood as well. And think through the wall colours and the budget for new lighting (as in adding 50% more lighting).

Is this the only doorway where the two types of flooring will meet? If so, I think you have more flexibility to choose the type of flooring that you want to have in the other spaces, whether hardwood or tile. If you want tile, I'd choose something that is a stone look tile, but I think you could make real hardwood work if you match the color as closely as posssible. However, if you have other big areas where these two types of flooring will meet, I think you need to use a stone look tile.