Not anymore. Try writing 10000000000000000000000000000000000000000000000000000000000000000000000000000000n + 1n into your browser console.
>JSON.stringify(1n)
TypeError: BigInt value can't be serialized in JSON
>JSON.stringify(1n)
Uncaught TypeError: Do not know how to serialize a BigInt
at JSON.stringify (<anonymous>)
at <anonymous>:1:6
Javascript can do arbitrary precision integers now. So the last part is not true. You can generate your JSON strings with string concatenation in JS if you like.
Just because JSON.stringify has some limit doesn't mean JS has.