It is possible to run your own relay, but is very expensive. Unless people decide to run their own relays, Bluesky is technically centralised. You can run your own PDS for cheap through.
It is currently early access, but should be opened to everyone later. There is also a bridge that links Bluesky and Mastadon. https://docs.bsky.app/blog/self-host-federation
I don't think there are public servers, but there most likey are private server for users who don't want to share there private info such as email, birthday, etc.
Yeah, Bluesky has both federation and ease of use, which is why many prefer it over Mastodon. Instead of making someone search for a server to join, Bluesky gives you a default server which makes it easier for less tech savvy users.
Below is how account portability work between servers, it is easy to migrate between servers.
Account portability
We assume that a Personal Data Server may fail at any time, either by going offline in its entirety, or by ceasing service for specific users. The goal of the AT Protocol is to ensure that a user can migrate their account to a new PDS without the server's involvement.
User data is stored in signed data repositories and verified by DIDs. Signed data repositories are like Git repos but for database records, and DIDs are essentially registries of user certificates, similar in some ways to the TLS certificate system. They are expected to be secure, reliable, and independent of the user's PDS.
Each DID document publishes two public keys: a signing key and a recovery key.
Signing key: Asserts changes to the DID Document and to the user's data repository.
Recovery key: Asserts changes to the DID Document; may override the signing key within a 72-hour window.
The signing key is entrusted to the PDS so that it can manage the user's data, but the recovery key is saved by the user, e.g. as a paper key. This makes it possible for the user to update their account to a new PDS without the original host's help.
A backup of the user’s data will be persistently synced to their client as a backup (contingent on the disk space available). Should a PDS disappear without notice, the user should be able to migrate to a new provider by updating their DID Document and uploading the backup
Bluesky is Decentralized, people are moving to Bluesky because it is easier to use and has better UI and UX. The reason people are moving to Bluesky and not mastodon has nothing to do with Decentralized, it is because it is simply user friendly. I used both and I think currently that Bluesky is definitely better. One of the biggest issues is the app, many users use their phones and The mastadon apps are awful in comparison to bluesky.
https://www.hostinger.com/tutorials/how-to-host-a-bluesky-pds
Bluesky uses AT Protocol and Mastodon uses ActivityPub which makes it impossible to federate. Bluesky does allow you to host your own servers though, so you can consider its own fediverse.