Hi Maria, we love the wood but it is a little overwhelming in that space with the timber floor. A liming white is a great idea as mentioned by a few people here. This will let you have the best of both worlds, a lighter, brighter finish while still allowing the wood grain to show through. You could try Feast Watson Liming White Floor Finish (yes, it's not a floor but it has the size of a floor!) and build up the number of coats until you are happy with the amount of timber grain showing through. You'll probably need to give it a light sand first as it's most likely already got some type of coating on it. The other option would be to leave the walls as is and consider a large, light neutral coloured rug as pompom suggested on the timber floor and perhaps a good sized piece of art on the wall or white wall shelving instead of the dark side unit you have to reduce the amount of timber in the room.

I would just paint the same colour but in a semi gloss

Disclaimer -- I hate grey with a vengance . So i may be biased . But if you scroll up , and get the 'luxury planking' at the top of your screen , and the Perfect Boredom at the bottom ( the heading thing cuts through the middle ) it looks horrible IMO . In the middle photo , the darker timber and the white actually makes the grey almost acceptible as a base , but look at the other pics , and even the floor is looking as grey as a corpse with all the colour washed out .

I like the colours you’ve suggested. I find neutrals restful. Do you have a sample of your cabinetry? An easy way to get a coordinated look, without whites clashing, is to have the white colour matched at the paint shop to the cabinetry. The colour match will tell you if White Beach is on the right track. I’d consider a more plainer white for the trim ie Natural White as suggested above or Berkshire White. For your splashback - could the budget stretch to the benchtop material? If not a tile colour that picks up one of the benchtop fleck colours will give you a coordinated look. Sounds lovely. Come back and post the completed pics.