Do not expose internal state in the public encoder API (i.e. as_json)

See [1] for why this is not a good idea.

As part of this refactor, circular reference protection in as_json has
been removed and the corresponding error class has been deprecated.

As discussed with @jeremy, circular reference error is considered
programmer errors and protecting against it is out of scope for
the encoder.

This is again based on the excellent work by @sergiocampama in #11728.

[1]: intridea/multi_json#138 (comment)