You need some way of serialization that makes clear it was serialized as a BigInt and thus must be de serialized as a BigInt without the likelihood of it misinterpreting the data like 9n being a tractor model. A single indicator would be too error prone, so the schema has to be more complex. With that complexity it needs to perform and be (cheaply) verifiable.
Quickest thing I can think of is storing it as power of 2 + the difference ending with character n as good measure. It is easy to serialize/de-serialize and you can verify the number by re-serializing to be a proper BigInt and not for instance a String. Confusion still would be possible, but rare. So 1 would be stored as 0+1n, 42 would be stored as 5+10n, etc.
If you only decoded big ones as BigInt, you would have the same problem of updating the code but now you have 2 codepaths at every callsite!
It's perhaps a defect in the JSON spec that it doesn't have a provision to support BigInt, but it's not really clear what should happen!