Their app is open source, but it doesn’t give any instructions on how to self-host it, in fact it seems to not have been designed with self-hosting in mind given the forking section of the ReadMe:

You have our blessing 🪄✨ to fork this application! However, it’s very important to be clear to users when you’re giving them a fork.

Please be sure to:

• Change all branding in the repository and UI to clearly differentiate from Bluesky.
• Change any support links (feedback, email, terms of service, etc) to your own systems.
• Replace any analytics or error-collection systems with your own so we don’t get super confused.

The impression I get from Bluesky is that it doesn’t view federation as a core feature of its platform, just a nice technical oddity. I’m no expert on the AT protocol, but from a quick skim of the quickstart, their view of federation seems to be having disparate data repositories (Personal Data Servers) app developers can put their app data into. It doesn’t really seems to be about different software communicating with each other.

In contrast, ActivityPub is about passing JSON between servers in a somewhat standard format so different software can reasonably understand what that JSON represents and act on it in a way that makes sense for that software.

(But again, I’m don’t know anything about the AT protocol, I could be completely wrong here)