I have the same problem upstairs, except it is a bathroom. LVTs clash with my oak bathroom vanity. I have been looking for 3 years. I am using carpet in my bedrooms that touch the oak wood floor in the hallway.

I agree that oak hardwood to match would be best, but if that can’t be done ( I couldn’t when we tried to match, maybe needed someone more skilled, idk ) I’d get Flor carpet tile, easy to switch out if a disaster happens on the carpet , I forget what it was, some product in blue for kids, but had to replace an area rug.

If you are installing LVL i will suggest a cooler toned gray or brown to provide contrast with the oak flooring in your hallway.

Match the hallway get unfinished flooring and have it finished to match . IMO no LVP will work well next to real wood.

As suggested, get unfinished wood flooring and match it to existing wood flooring.