Okay, so the PDS handles personal interactions, and your verifiable identity is stored on a (currently centralized) registry. What else? There's a set of account features the protocol lumps under the heading of "big world" networking, which includes "large-scale metrics" as well as algorithms and search. Those are handled by indexing services that crawl the network collecting information. Basically, Bluesky will be running its own Google for the whole network.
Consent-based indexing is a hot-button issue on the fediverse, so the fact that Bluesky needs large-scale indexing to function is probably already a big red flag for many of you. But what are they indexing, exactly? Well, that "large-scale" metrics category includes likes, reposts and followers (which it would have to, in order to serve algorithms), so in effect, your entire social graph is being constantly indexed in a cloud somewhere at all times.