One idea is to paint all the wood including the media cabinets and the wainscott a light tone of grey and the walls white. Do you want the columns/posts to stand our or blend in with the wall? If you want them to blend in then you can do them white. If you want them to stand out then you can do them grey too. Additional small tip:not necessary but if you wanted to, you could consider changing the round column to a white one so it matches the other to make it uniform. I think it's a great space with the nice flow and I think it will turn our beautiful :-)

Below are pictures of my basement. Looking for a light and bright color for the space that doesn’t make it look stark. I included a picture of swatches I brought home which looked totally different in store. I also tried Alabaster by Sherwin Williams on the wall but unsure if it’s too yellow/warm and will clash with the gray tile.

IMO a daybed is not a good choice for an actual bed. I am tall and hate foot boards for that reason. As for the pink IMO never do a color for a permanent piece in a kids bedroom since the favorite color changes yearly . get a nice neutral headboard on a regular bed get a trundle if you need the extra sleeping space and then get pink bedding that can be changed next year . Why not get a forever bed and save the money for the changes that are coming.

Everything is OK for as long as it's OK with you and the look you want.