I would look at a luxury vinyl tile in a wood effect. Most of them are textured so aren’t slippery and warmer than tiles. If you go for tiles rather than a sheet I think the only drawback is not letting water pool in the joins plus how realistic they look varies even between the same make but there are a lot of good ones

We're mid rennovation and currently having big floor level dramas too. Want to retro fit underfloor heating but need a similar floor level to the existing suspended floor boards and the new extension. It's really tricky! Personally I wouldn't do lvt herringbone as for me it would never look as good as the real deal. I'd go for another vinyl pattern or possibly engineered wood planks. There's some lovely examples of unique thresholds on here and Pinterest so you could be creative and make a feature of the join area.

For me, it could be too busy and distracting for some floors/rooms but that depends on what the layout of the house is and how the rooms are decorated. As Sonia says, look up an earlier post where the herringbone floor was lovely, but because of the angles in the house, she couldn’t stand the pattern.I have herringbone floor tiles in 2 bathrooms, which I like, but knew I wouldn’t want it downstairs because of tongue and groove ceiling in one room and too many angles in another - the effect of herringbone would not have felt relaxing to be in.

There tends to be more waste with herringbone, so you will need to allow for this in quantity of flooring required as you often will need more flooring than when laid straight. Although it may look straightforward, depending on your room shape, it can be complex and very time consuming at the edges. I found this which looks helpful https://www.directwoodflooring.co.uk/dwfblog/how-to-lay-herringbone-laminate-flooring/