You can easily find drop bars in 25.4 mm clamp diameter. In the end, you may decide on a different stem anyway if you aren't happy with the position of the new bars. I'd get 25.4 drop bars and try them. Just budget for a second stem in case you want to change the reach or angle of the stem.

You will need new brake levers. Not only for the curved nature of where the brake levers mount on drop bars. Also because MTB and road bars have different diameters where the brakes mount. Make sure you bet brake levers that are compatible with your brakes. V-brakes, for example require a brake lever that pulls more cable and has less leverage built into the handle. I'm not sure if there are any road brake levers with that characteristic.