Sorry but you will need to remove the tile and IMO the best choice is unfinished woof flooring in the sam especies of wood as the old and then have the new finished to match . Laying new floor over the old will result in a tripping hazard that tiny bit of difference in flooring height is worse than an actul step.

I also would replace the tile with the same species of wood. You can have the hardwood guys feather it in with the existing floor and you'll never be able to tell it wasn't always like that. LVP next to that flooring will always say, "Hello, we were installed a couple decades apart."

I agree with Patricia and Julie

Agree that LVP and real wood together never looks right together and the larger thresholds (since you would be going on top of the tile) between the rooms will make the house feel cut up and smaller. if you are not up for matching the hardwood then i would simply replace the tile - something that looks like a classic slate could work

LVP next to real hardwood looks terrible. It just enhances the fakeness of the LVP. Do this right by removing the tile and installing identical hardwood to what you already have. Then have it all finished to match. I agree with a previous poster that short of that, slate would work.

We are in the same boat as you. But after many agonizing weeks and months of reading, researching, flooring stores, etc., we are installing LVP. Yes, I know it will not match my wood floors, but I am not trying to fool anyone into thinking it will, so I chose something lighter and brighter than my current wood floor.

Between 3 very messy teens and a giant derpy dog, wood floors in my kitchen and entryway and just NOT an option. My family room wood floors are too newish to replace, and I can not physically move out of my house for several days to place the kitchen with new tile. I think just accepting that the two floors for what they are is just going to have to be fine. I am not creating a Showhouse, or displaying my home on social media, nor am I moving any time soon, so I am going to do what I want!

IMO a viyl stone look would have been a better choice .