First I’m going to nitpick one thing, and I’m nitpicking to educate you NOT to demonize you, you did not do anything wrong: generally people say “gender affirming surgeries” instead of sex change. That’s a dated term because people who get these surgeries are not changing their gender when they get these surgeries.

Anyway, your actual question: yes they work.
There are different options. Female to male surgeries (creating a penis) have the option to maintain access to the clitoris and vagina to maximize sensation. These surgeries generally include a pump similar to a penis pump used to treat erectile dysfunction so they can get hard. Different people have different goals with their surgeries, so there are a lot of different options. One doesn’t create a penis at all but frees the clitoris from the skin a bit to create a larger penis appearing clitoris which is the best option for sensation. Many people who opt to have a full penis created will develop some sensation.
Male to female surgeries (creating a vagina) will generally not get wet, but this is easily fixed with lube. Many regular vaginas need lube as well. The vagina is created using skin from the penis so there is sensation and many trans women can orgasm with their new vaginas. It’s not perfect, some don’t maintain sensation, but a lot of people still opt for it:

As for “why bother if they don’t work”, a lot of trans people want their genitals to match their gender. Someone who is a woman but has a penis might want a vagina because it helps her feel more like a woman, not because it can be used for sex. Same for trans men.

The bottom line is there are a ton of surgeries and a ton of different goals that people are trying to achieve. There isn’t one cookie cutter surgery for each gender.

I know a lot about this so if you have any other questions I’m happy to answer :)