The MongoDB shell speaks Javascript, so the answer is simple: use JSON.stringify(). If your command is db.serverStatus(), then you can simply do this:
JSON.stringify(db.serverStatus())
This won’t output the proper “strict mode” representation of each of the fields ({ "floatApprox": <number> } instead of { "$numberLong": "<number>" }), but if what you care about is getting standards-compliant JSON out, this’ll do the trick.