If you want to match the inspiration picture, carbon gray gel stain is more blue than espresso. What’s pictured is probably a mix of antique walnut and black. Paint js much easier to control and get the color your want.

Replace the whole thing; in any color, it screams "dated". If you decide to choose a metal railing/balusters, the one pictured looks too bulky and "outdoorsy", so look for something visually lighter. If you're home is modern all the way through, maybe consider a cable stair railing.

you can't just apply a gel stain on top of the current stain. (well, you can, but it's not going to adhere properly and will end up looking like poo).

anytime you stain wood, you have to remove the current finish, especially the clear coat top coat. And since I can see a glossy finish on them, they do have a protective clear coat. a new stain will not penetrate that.

It's a ton of work to sand every inch of those wood stairs to remove that top coat, and underlying stain color. That's the only way you're going to get a true carbon gray color.

either replace the balusters w/something different, or, just use paint.

you can sand the handrails and base and stain in a java, paint the rest white

i'd replace them w/simple square spindle like these

or, go for the metal

here's a similar before and after

Listen to Beth. gel stain over a glossy finish just looks clumpy and uneven (I've tried it on a small project, and OMG, never again). Replacing it will be the best looking option. If you really can't afford that, paint it with a soft black paint in gloss or satin.

If you replace it, you might be able to donate the old one to habitat for humanity.