Let me give a quiz. What's the thing which "itsy bitsy," "pizza," "Nazi," "bankruptcy" all share?

It's the /ts/ sound.

But I don't know if English native speakers perceive this sound as two distinct constonants or a single consonant.

Which way do they perceive it? Is it "it-see bit-see," as they are hyphenated in the form it-sy bit-sy? Or as "its-ee bits-ee"?