For those still looking - Scion has a good mix of Scandi wallpapers https://www.wallpaperstudio.com.au/brand/scion

We have installed wallpaper behind glass splash backs on many occasions without any problems, the glass usually being attached by a thin beading of clear silicon applied around the inside perimeter of he glass, then fitted the day after the wallpaper install. MOST importantly the INSIDE of the glass be kept perfectly clean on install as even fingerprints will stand out

Can you provide a picture of where you're planning to put the paper vs the paint? I think, myself, that wallpaper should be continuous along the length of the wall, unless there are architectural features that break up the line of sight.

As I said before keeping clutter under control is the key, get lots of storage ,you said cost is I s an issue. Look at IKEA they have solutions for wall units that you can get in different colours and that in itself will brighten the place. You would benefit from a buffet next to the kitchen /dining area or a large wall unit with lots of shelfs and drawers, coffee table with storage drawers , storage unit with baskets for kids toys and school stuff, once you have this under control start adding rugs if think you still need it. By the look of it you have small kids get them to put things in appropriate place and get some funky coat hangers in the entrance so they can hang hats and bags etc.