Post a PHOTO.

Putting wood/wainscoting in a bathroom is not a great idea -- most wood really doesn't like a lot of moisture. That doesn't mean you cannot have the look of wood wainscoting -- perhaps along the window wall:

https://www.wayfair.com/eJoy--28-x-28-Peel-and-Stick-Soft-Foam-Wall-Paneling-BrownWoodGrain10PC-L7279-K~EJOY1858.html?refid=GX340335595086-EJOY1858_38180254&device=c&ptid=673621604359&network=g&targetid=aud-354999624431:pla-673621604359&channel=GooglePLA&ireid=72971647&fdid=1817&PiID%5B%5D=38180254&gclid=EAIaIQobChMIt9CigMCd5wIVh5-fCh0EhAqHEAkYASABEgLpbvD_BwE

Since you don't like the tile ...

Although the tile is not unattractive, adding color to the room could help the look of it and, to some extent, make the tile you don't like visually "disappear" -- or at least not be emphasized.

If you go with the faux wainscoting, you could paint that and your window trim white, then paint the wall above that wainscoting your favorite bold color. You might want to keep the rest of your walls and vanity the same neutral color -- a color from within the tile -- so your accent wall and window are the focal point of the room.

Not a pro. My thinking is go with what you truly like.

( If you want bold red or blue walls, paint them that color, however,)

You might be better served using your shower curtain to make any drastic "change" to the color of the tile side of the room while keeping most of your walls a bit more neutral. That said, there appears to be enough tan/brown and yellowish in the tile to consider adding green as your wall color or just use a truly great bright yellow.

Get some construction paper or card stock and paint it the different colors you might be considering and tape them to the tile-- individually or w/space between them -- to get an idea how they'd look to you.

The light in your room can also make a difference. Before choosing your paint, consider swapping out the bulbs for your lighting and see if that makes a noticeable difference.

I was expecting something awful, but it's not bad at all. The issue is the gray paint, which will not work. Some of your inspiration photos lean that way, but you're correct that something in the cream/warm family would look better.

Some pros may have suggestions for stronger colors, maybe sage walls and cream vanity or something.

Another option for you would be wallpaper, if you have decent ventilation. That could provide a statement that would take the focus off the tile.

One thing I've observed is that handicapped people can take a toll on bathrooms, banging into walls and such. That was certainly the case with my in-laws. My MIL had her bathroom festooned with grab bars - like a dozen of them. We had to retile the whole bathroom before selling the house. You may have to fill holes in the wall and trim, but that is easily done and will look great after.

By contrast, your two bars aren't bad at all, and will work well as towel bars.