Which version of Safari are you using? According to caniuse[0], arrow functions are supported in Safari starting with version 10, which is over four years old at this point.
They said "arrow function methods", so I assume they're looking for public class fields support [1], not only arrow functions support per se. Public class fields (apart from static fields) are also supported in Safari though since September.
Yes, that's exactly what I meant! Nice! Indeed, I had in mind a script I wrote just around that time and I guess the iPhone I was testing on was not fully updated. Just checked on my Safari on Big Sur and they do work now, sweet ! Should have tried / checked before commenting, thanks for the heads up ;)