My own bird gives the impression of having to stop and go into a slow think-it-through mode. If the brain trades sequential processing for parallelism, you could be arbitrarily smart at the cost of taking a long time.
Since it’s the connections (wiring) that takes most of the room in a human brain, suppose you instead use small cells of addressable memory, to store state. The amount of storage could be greater than a human brain.
Does intelligence require copious memory? Great reasoning skills and the ability to run hypothetical situations could be quite smart, even if he can’t learn everything needed for an advanced PhD.
Can't measure it on a human IQ. It’s not a single scalar number. Test human subjects on ability to memorize and recite huge amounts of music, remember perfectly several hundred seed cache locations, and they will do poorly. The bird doesn't have the language hardware so testing the linguistics is unfair. problem solving using geometrical relationships, cause-and-effect sequences, and objects in the environment: it’s perfectly plausible to build a bird-sized brain that exceeds a human’s skill at that.