One thing I still didn't quite grasp with BlueSky yet is if it's a decentralized platform or not... ATProto seems technically capable of supporting decentralized platforms.
IMO the devs have been so overburdened with trying to nail moderation that they're actually disincentivized from onboarding new populations, since multiple entry points to the network just lands in their lap as more difficult moderation problems - that is, they're still figuring out how to moderate people on their own servers and haven't yet decided how they're going to moderate with a federation of servers with different cultures than their own
I don't think they're avoiding the big problems, but it does seem like they're taking the slow careful route, maybe this is for the best.
Unlike Mastodon, you don't have people running copies of the Bluesky app because it is simply unnecessary — each copy would "see" the same network. If you wanted to fork the Bluesky product (e.g. different branding, different moderation decisions, different product decisions) then yes, you'd run your own product on your own backend and it would be able to ingest Bluesky app data (and vice versa, the Bluesky app would be able to ingest the data from your product).
That platform is (today) a centralized walled garden. As others detailed, it is difficult for anyone to add new servers and even more difficult to convince the official client to support them.
It is a complete contrast to NOSTR that has zero official servers and zero official clients to access the data. It has hundreds of relays from different people, along with several clients from different developers that compete for your preference.
Twitter also had 3rd party clients until one day they turned off the switch.
Around NOSTR there are no labels as "3rd party clients" because they can't lock down your data with the push of a switch nor block your use of the platform.