How many bits of plaintext are required to verify a stream cipher key? If a stream cipher has an $n$-bit internal state, how many bits of known plaintext are required to confirm that particular key is the key?

I believe that the answer is at least $n$-bit's of plaintext. My reasoning is that an $n$-bit state would allow it to generate at most $2^n$ different key-streams, assuming it was a perfect bijection onto the first $n$-bits - which it probably isn't. Is this correct?
At least $n$ typically more. If you have no IV, as in classical setups, you need to do a state transition analysis. If there is an IV then the (key +IV) mixing phase also needs to be analysed and the answer is most likely probabilistic.

In short, the bijective mapping you're talking about is very very rare in a well designed stream cipher.