You can paint the trim, and the door, just paint the inside and leave the door edge and the other side oak.

These are small suggestions. Changing the faucet fixture can shift the appearance quite a bit. Also, instead of decorating picking up the black, focus on something else (sounds like you do not care for the wood) but for example, if the mirror was framed in wood it would feel warmer, and if the art didn't pick up on the black. The black can look and feel a little cold.

I would paint the cabinets white and not worry about changing the bathroom door. Paint the trim if you want. Maybe add metal hardware to the cabinet doors. I would replace the faucet with a two-handled version (less convenient but much prettier and not terribly inconvenient when you get used to it). Add a vase of fresh flowers on the countertop. Decorate with beautiful plush towels, maybe white or gray or an accent color you love. (I am not fond of decor on top of the toilet - sorry!)

Google "black and white bathrooms" to see if you can get more ideas. You can change the paint color too. If you want to start making an investment, look at changing your countertop/sink and mirror. But if you are planning to do a complete remodel, wait on the countertop, unless you find an inexpensive temporary option.

I'd either paint the cabinet white or black (or use General Finishes gel stain in espresso) or gray, then get a new faucet. Personally, I like the hansgrohe from Costco for 80.00. Probably would paint it gray to have some contrast with the top --- unless you replace that with a separate vanity top, which opens a lot more options.

Get a black and white runner and black and white artsy photography.

And then some white orchid.

I actually like that black racing stripe :)

You can paint the cabinet, and leave the doors and trim stained. I did that in my house and it looked great. With the black top, I recommend a cream paint for the vanity. It will blend well without looking too stark. I went back several yrs later and painted all of the doors cream also, but left the frames stained oak and it looks terrific. It brightened the entire house up so much.

I would remove the shower door & go with a curtain. Also I would replace the art & mirror. If you don't want to replace the countertop I would get rid of everything that draws attention to ti. The black is very harsh to the eye.

On my monitor, the floor looks positively pinkish.

If you can't/won't change the counter, I'd paint the walls a softer gray that goes with the floor and the vanity a darker shade gray.

Like this but because the counter is black, I'd paint the vanity gray. Any accessory colors.

Or paint the vanity white and go with whatever other color you want, even white or dark.

If you replace the doors with a curtain, you could also keep it closed and don't worry about the black accent tiles.

Change mirror for a wood or brushed nickle. I'd decorate with art that has bright yellow, and add bright yellow/white towels, and maybe a bright yellow/white/black shower curtain. That would brighten it and warm it up. Bright yellow, black and white look awesome together.

White countertop, new nickle faucet, new mirror with nickle edge. Paint the brass frame nickle or remove and use a curtain.