I'm looking for a word for someone who doesn't want you to succeed or threatened by your success.
Particular for fear that your success will overshadow their own. Not so much for malicious reasons, but more from insecurity.
Someone suffering from tall poppy syndrome.
Tall poppy syndrome (TPS) is a pejorative term primarily used in the UK, Canada, Australia, New Zealand and other Anglosphere nations to describe a social phenomenon in which people of genuine merit are resented, attacked, cut down, or criticised because their talents or achievements elevate them above or distinguish them from their peers.
Sue was suffering from tall poppy syndrome. After her cousin Kathy landed a high paying modeling job in New York, she complained loudly at the family gathering about how 'Kathy thinks she's so much better than us now that she's working in New York. Pity it's not going to make her an any nicer person'.
How about Rival? Adversary? Frenemy? Hater?
The obvious, to me, candidate is nemesis, from the Online Merriam Webster:
a : one that inflicts retribution or vengeance
b : a formidable and usually victorious rival or opponent
I think opposition would work well.
Defined: a group of adversaries or competitors, especially a rival political party or athletic team.
If someone is your opposition, they would likely want you to fail, so that your success doesn't out shadow theirs.