AP intercompatibility is fun, but it starts to fall apart once you leave the safety of the "Note" (statuses) and "Question" (polls) types (which is what Mastodon, Pixelfed, Misskey, Pleroma, etc. all use as their primary elements). Everything outside of it becomes either loosely converted to a note (Mastodon does this for a lot of things, see https://docs.joinmastodon.org/spec/activitypub/#payloads) or is discarded by the instance. The only types that I know of which have been able to have native support from multiple AP implementations are micro-blogging and Lemmy's community system, with everything else essentially being a monoculture (or just extremely one-sided towards a specific implementation) due to a lack of interest from other implementations in providing full, standardized support. This isn't an inherent protocol limitation, but I do think that the community could do better in organizing standards outside of the core documents.
ATproto's system is a bit more well defined (you HAVE to abide by the lexicon/schema of the data collection to be accepted by implementations, reference implementation and some third-party ones have schema validators to do so) and allows for easier intercompatibility, but I do think that it could be a bit looser than it is right now (selective support for additional fields) to provide proper "sidecar" values in a record (they'll be in the user's PDS but it won't validate and could be rejected by indexers). Bridgy Fed does this to include the originating URL from APub and the original text, which third-party clients could certainly take advantage of if they detect that the post comes from a Bridgy account. (https://fed.brid.gy/docs#bluesky-fields)
You're welcome. I understand that a lot of what I've said is technical jargon and nonsense to the average *.bsky.social user but a lot of it can be simply dumbed down to "the client can choose to ignore it" or "get off Bluesky servers, lol?".
At the risk of sounding like a shill, I would also say that the protocol is much less mature than ActivityPub or Nostr, but the rate of progress that I've seen is pretty rapid (compared to APub at least, Nostr is also a rapidly-developing protocol but its harder for me to track its progress as there's no reliable source for protocol updates that is not on Nostr afaik) and with the active developer community surrounding it I firmly believe that most of these issues will be solved within the next few years at worst. Zeppelin has also progressed on bringing back some of these missing features, as video processing and chat have been introduced to the AppView (albeit proxied through Bluesky's services so it's a moot point).
There's an important distinction to make between AppViews and an APub instance, which is that AppViews handle solely the application portion of the user experience while APub instances typically manage the entirety of the user's experience. As a result, ATproto users can hop between any AppView without any lock-in to a specific AppView provider as their accounts aren't bound to their existence (which means that anyone can switch from using the Bluesky AppView to the Zeppelin AppView with little difficulty (or any other AppView)), while users on the Fediverse cannot easily do the same (applications can authenticate with a Fediverse account to confirm their identity but there are limits to what you can do, such as federating with the identity of that user). They're also not designed to be closed/single-user instances, mainly because the PDS handles the role of user management and platforming users and is where most of that responsibility is placed at. In regards to active usage, enough moderation controversies have happened with Bluesky Social's policies to the point that a small (at this moment) market has opened for a Bluesky with truly user-controllable moderation, and that Zeppelin will be one of the main products to serve that market. The costs also aren't that large compared to some of the larger Mastodon instances, so for the amount of content that it's storing it could be way worse (mstdn.social saved 180 euros when moving to another server apparently but there's definitely other examples of Mastodon unnecessarily ballooning instance costs as it grows in scale, because it's bloatware compared to what's out there. mstdn.social is also a fraction of the activity size of the ATproto network's output on off-peak hours, so eh).
I will say that this isn't a core attribute of the Fediverse, the base protocol is only slightly less extensive and modifiable than Nostr as projects like ActivityPods and "nomadic identities" (over a decade old!) exist which can perform a similar role to an ATproto PDS but with the Solid protocol but it's seen little adoption due to the lack of focus towards implementing "next-gen" features like these in the current set of APub server software.
I think that your description of ATproto relays is a conflation of the role of an AppView (or backend) in ATproto and a Nostr relay. Relays (by default) are not designed to be a permanent archive of content, and are really meant as content streams for backends to ingest and index appropriately. The storage cost is also overestimated, as people have begun to host third-party variants of the Bluesky AppView (which is partially open-source due to its dependence on internal code for some non-essential to microblogging functionality): https://whtwnd.com/futur.blue/3ls7sbvpsqc2w
The note at the end about Bluesky being able to censor, verify and ban users from the protocol is also largely incorrect, with some asterisks as is for a complex system. The Turkish accounts that were censored were hidden from the platform in Turkey via the app's labeler system, which allows for "composable moderation". You can use this system to implement geoblocking in Bluesky clients based on your IP address when you open the app, which is what they did to ban those accounts from being seen in Turkey. The application of labelers (outside of Bluesky's main moderation service which the Bluesky-hosted AppView follows) is client-side, and any client that doesn't want to respect the default geoblocking behaviour (or implement mod labels at all) can just ignore it.
The Politico columnist that was banned from Bluesky has their account taken down from the whole network because their account was hosted on a Bluesky PDS, which could be (somewhat because, again, the default AppView follows a default labeler for displaying content through the AppView's API) bypassed by moving their account to another PDS that isn't operated by Bluesky. If your account was banned from Bluesky while also being on a non-Bluesky PDS, you would still have access to the ecosystem (and a half-working version of Bluesky that is basically a shadowban due to the default client and AppView conflicting with the labeler's takedown action).
Speaking of PDSes, they also do quite a bit more than just store user data. As an user's identity is dependent on a PDS to exist as a proper account, most user actions have to be routed through it to allow applications to store their data on-protocol and to authenticate the user.
The verification system is implemented through a record type (or "Lexicon") that is stored on an account that basically confirms that the record owner has verified the target. The system is also odd in that there are two types of verified accounts, "trusted verifiers" (think Twitter's business verification system) and regular verified accounts. Trusted verifiers are chosen by the client and can verify their own set of accounts, giving them the regular checkmark. Clients that haven't implemented support for the checkmarks or allow users to choose their own trusted verifiers can basically see whatever checkmarks they want, or just disable the system altogether (which is possible in the default client).
How Bluesky uses DIDs are... complicated. ATproto supports two DID methods for accounts, did:web and did:plc. Web DIDs are used mainly for services on the network, but can also be used for regular accounts. PLC is a more complicated system, which becomes quite obvious when you find out the original acronym meaning was "placeholder". PLC is (in regards to the general protocol) not a decentralized system, as its current iteration is a DID document pastebin with authentication and version history. I do think that the method's current centralized status can be mitigated somewhat (synchronization between various directories, then having a consensus system for establishing the validity of the documents' current states), but the system could always be replaced at any point to either incorporate new features or to choose a new model for how documents are publicized.
Sorry for the long read but as you see I've wasted way too much time into reading through developer posts and documentation, had to unload it somehow.
ATproto's system is a bit more well defined (you HAVE to abide by the lexicon/schema of the data collection to be accepted by implementations, reference implementation and some third-party ones have schema validators to do so) and allows for easier intercompatibility, but I do think that it could be a bit looser than it is right now (selective support for additional fields) to provide proper "sidecar" values in a record (they'll be in the user's PDS but it won't validate and could be rejected by indexers). Bridgy Fed does this to include the originating URL from APub and the original text, which third-party clients could certainly take advantage of if they detect that the post comes from a Bridgy account. (https://fed.brid.gy/docs#bluesky-fields)