Who cares. It's a private bathroom, only you and family see it.

Brass is "gold" and always the traditional choice for faucet metal.

Good and chrome would NOT look good together. At all. That's something a realtor is going to point out to you as well when it's time to move. I would simply change out all the fixtures.

The answer is “Do what you like, it’s your house”.

Change them out. Even spray paint them

I recently completed 2 bathroom renovations in my home. From my readings, you don’t want one outlier metal in the room. Think about where else you could add gold in the room. For example, a mirror or light fixture or cabinet hardware. Both google and Pinterest offer completed bathrooms.

Yes. it would. A gold faucet would stick out like a sore thumb.
Not to mention the finish may or may not last.
Chrome is classic. Can you do a gold mirror instead?

My 12-yo daughters needs to have her bathroom faucet replaced. Currently, the fixtures in there (faucet, shower curtain rod, shower fixtures) are all chrome. She would like to move to a gold tone, which actually would look good in there. But, I don't want to have to change all the fixtures.

Do you think it would look bad to have a gold-colored faucet in the sink and chrome shower fixtures? Or, does everything have to be the same color?