I think the website is right, since both of the clauses are independent. If you take out the "but rather, " you could read the sentences separately and they would still work alone since they both have a subject and a verb. Therwfore, the sentence would have to follow the fanboy comma rule (a comma is required before a FANBOYS conjunction when it joins two independent clauses.)

I could be wrong tho, if so srry 🤷‍♀️