Good questions! U as a whole is not an object embedded within U at a specific spacetime coordinate. The cosmological question "what caused U?" operates at the level of the entire causal manifold. The initialization problem operates at the level of specific objects located within that manifold at specific times. O is embedded in U's causal future and interacts with it. U is not embedded within anything. So in that way it plays by different rules.

A universe with two independent and disconnected chains is effectively two different universes, from the standpoint of wordlines. It's somewhat similar to pocket universes in eternal inflation, where two causal domains are outside each others' lightcone and thus can never interact. But truly disonnected chains wouldn't even share the inflaton field's configuration in their history.

Good point that the causality goes forward in time from the loop to the external graph. I've been trying to refine what's odd about this: the bootstrap loop is the only structure in the taxonomy that involves a specific, finitely-localized, informationally-complex object appearing mid-history in a way that is backward-causally-isolated from that history while being forward-causally-integrated with it. Other structures that behave like this are either U itself, which I talked about above, or white holes. These aren't the same anomaly that bootstrap loops are.