When I say “the cat is possibly inside, possibly outside, and actually inside

To me that is a logical impossibility as stated. But it is a matter of interpretation. In conversation you might just mean there are two possible conditions and it is currently one of the two. The word possibly implies a probability or uncertainty.

If you modified and said “the cat is possibly inside, possibly outside, and it is probably inside" That would make sense to me. An expression of probability. The cat is in one or two possible places, I expect it is one of the two. Informal reasoning.

Or“the cat can be at times possibly inside, possibly outside, and I know it is inside inside"

Semantics and cone text vs mathematical probabilities and informal erbal reasoning.

Toss a die in the air, until it comes to rest on the floor there are six possibilities. Once it lands and is stable there is only one possibility. Ignoring ending up on an edge or a corner.