Hmm. I think you're just going to have to replace them altogether. Look for widespread faucets that have narrow bases for the handles.

Or, if you don't like the integrated sinks, you can replace them with new countertops, an undermount sink, and then get whatever lav faucet you want.

I would not paint them - but it would not be expensive to replace the towel bars and TP holders so I would start there and then replace the faucets down the road - I have donated lots of bathroom fixtures to Habitat Restore and that way they get used

Paint would just chip off on the faucets. That two-finish style was popular in the 1990s, so your faucets may need replacing soon if they are worn from regular use. Sometimes the same faucet style was made with three handle choices: shiny brass, white porcelain, or chrome. You may be able to find replacement handles (and drain pull knobs) if you check with the manufacturer. Then you'd have less to ignore on the faucets until you are ready to replace the whole suite of bath hardware.

IMO you will need to scap them or at least take them to place that sells used fixtures .I didlikr towel bars so I just use hooks and the faucets are easily repalced the only thing is the holes for the old ones . You will need to meaure those and make sure you can either cover them or use them. IMO this is all very dated so I think you need to figure out what your style is and then replace as you go with renovating.

Less expensive to update to a single-lever faucet with a mounting plate

The only durable fix would be to uninstall the fixtures and have them uniformly re-plated. However, this would be both a hassle and likely more expensive than simply replacing them with new ones in a more contemporary style.

Ha, we have that very same faucet (and used to have matching towel bar and toilet paper holder, though have since replaced those). I did spend some time about 10 years back hunting for handles that could be swapped out with no luck; we just decided to live with it until it could be replaced. Ours are from a cheap 90s big box remodel. I will say that I HATE the escutcheons on that faucet because they trap so much gunk with all the grooves, and that on its own is a perfectly good reason to replace it IMO. In our case we need to replace the entire sink anyway so I'm just waiting to do it all at once. I might consider replacing yours one bath at a time starting with the one you will use most frequently.

If you can identify the manufacturer (Grohe, Moen etc) look on their website to see if they still make this style. If they do those parts could be swapped out with the polished nickel finish instead of the brass finishes. If this two-toned set is a much older one then you may be out of luck, but could be worth checking.

They are installed on very moderate hotel style and quality tops it would seem?

Before you worry on those and all other baths at the same time on a recently purchased home?

Slow down, post the most important bath...........yours. Your kids don't care. I would not buy a "replacement" anything, for any bath at this moment.

I think you are far ahead of yourself. Show the primary bath in entirety.

No.......you can't paint these, and no, not worth a refinish in ANY way. The Counter top in your picture is classic Holiday Inn. Probably not what you want, long term.

The knee jerk urge to replace, re do, every annoying ,not your style thing in a new home? Is a money pit of mistakes waiting to happen. Slow DOWN.

Personally I wouldn't replace these with something cheap just to get a different look.

Okay, if I decide to keep the brass/chrome combo fixtures, which style of bathroom light fixtures would work with them?

This is the master bath, the other two baths also have some version of this fixture. Above the light is a narrow window. Not sure if the shade is necessary, I may take that down, but we'll see.

https://www.build.com/moen-97372/s408531?uid=209319

https://www.moen.com/products/Monticello/Monticello_Chrome_twohandle_low_arc_bathroom_faucet/T4570

Look. It's a 1990 ish bath?

Paint the vanity. A soft green, a deep green? Paint the walls. White, green depends vanity. The floor isn't going soon, right?

Add hardware to the vanity, pick brass?

Frame in the existing mirror ( a handy man can do it with simple 1 x2 add two THREE light fixtures over the mirror.

You'll note I didn't say change the vanity top, or the faucets.

I'd save both for a larger improvement : ) Way up the road.

Is that a window or an art opportunity over that tub : ) ?

Point is, it's not the faucets alone, and faucets alone won't fix it to what you probably want long term. Start a piggy bank. You just moved in.

Jan, do you have any specific light fixture suggestions? That was my follow-up question.

Wall paint, cream vanity, hardware, framed mirrors, and a runner are already in the works. The changes will make the bath more up-to-date than 90% of the comps that have sold in the past two years. This ain't my first rodeo. My piggy bank is great.

Oh, guess I got confused with the earlier thoughts to paint the faucets. Well? If my " piggy bank was great"'? I might just go further and just get the bathroom I really loved. Given you're already addressing the other things mentioned.Depends if you want update to neighborhood comps or your own tastes for lights. Or anything else. Even the height of the vanity, which could be a bit low by newer standards? We don't know - hard to say from pics. Pottery Barn is a good value on bath lighting, and you'll find a pretty good mesh with the faucet style, multiple finishes to include chrome

I would definitely paint the vanity and add hardware.

Moen faucets are lifetime warranty as long as they are not used in a commercial setting, i.e. gas station rest room. I have a moen faucet thirty years old, called them and they do want a receipt, which I had but was too faded, scanning or taking a picture did not work, I told them I tried to copy but was too faded, They took care of me anyway. They did not have a whole faucet due too how old it was, but, they did have the parts I requested, they sent them free of charge and no s&h. faucet looks and works like brand new now.