I don’t think anyone can answer that for you. Generally, when I am attached to a character, it means the character’s identity, so I would definitely create a new character to play another race. But if you are not attached to the character’s identity but rather the class, what you have done with them, or some other aspect, but are not happy with their race, a race change would make sense.

There are so many different ways people play the game and how they view their characters, that I don’t see how anyone but you can know the best option for you.

There's no right or wrong answer here, only you can decide what's best for you. I think the only objective factor is that if you've got a spare character slot already then starting a new character is free, so maybe you could try that (you won't be able to use the exact same name though) and see how you feel about it, to help you make a decision before spending money on it.

Personally I'd always make a new character instead of race changing them, but that's because I don't mind repeating stuff and I'm not in any hurry to be able to use a new character for end-game activities, and because I like coming up with backstories and personalities for them and a lot of that would change if they were a different race, so I'd prefer to start over with a new character than try to convert an existing one.

But if what's most important to you about the character is what you've done with them and you would feel like you were losing more by starting all that over again than you'd gain from a clean break and restart then it's absolutely worth using a race change.

Even if the character as a person is important to you I think it could work. I've used one character in numerous games for about 20 years now and she's gone between human, elf, half-elf, "basically this setting's elves" and a few other things, changed class and skill set almost every time (even going from a game to it's sequel there will be differences) and her backstory is adjusted each time to fit the game, but in my head she's still the same person, so it could work with a race change too. But within a game I like to keep things as consistent as I can, so I'd prefer to restart.