Note: in hindsight, half of this post is answering my own questions as I explore this rarer side of federation, but there are still some remaining questions which I have highlighted.
Introduction
This post is created on lemmy.ml. The benefits of federating this post to other Lemmy instances is immediately obvious, since they can use most or all of the site features to read it as intended and interact (voting, replying, reporting, saving, cross-posting or browsing and subscribing to fediverse@lemmy.ml).
There is also intuitive benefit in being able to federate with other link aggregators such as lotide and Prismo instances. All these sites have the same basic interface of link-posting, text-posting, voting, commenting and voting on comments. The base format is very compatible, even if extra features are not. I wouldn't be surprised if Lemmy and lotide form a dynamic similar to Mastodon and Pleroma, two microblogging services which again have an intuitive base compatibility.
But what about different types?
What are the benefits of, for example, making Lemmy federate with Mastodon, Friendica or PeerTube?
One approach to answering that is asking what cross-interaction is already possible, like some posts in !feditolemmy which were posted from Friendica. This nerdica.net post which is also replicated on !fediverse shows a conversation in replies between a few Lemmy instances and a Friendica account, and demonstrates the clear analogue of our communities and their forums, and of our votes and their likes (it's just a test ;) )
So Friendica posts federating to Lemmy makes reasonable sense. I'm not sure about the opposite. I guess their posts are analogous to our text posts or text & link posts, so it might be possible to render their forums as browsable communities here.
Question 1: Does my Lemmy account browsing and making new posts on Friendica forums make sense? Or will the federation only make sense for enabling Lemmy to aggregate Friendica posts and allowing cross-rating and cross-commenting?
Note: I found this Friendica forum on Lemmy, which was properly interpreted as a community instead of a user by Lemmy, but posts aren't replicating yet. I'm guessing it's a base for future completion to allow further cross-integration. Friendica does not appear to be able to browse Lemmy users or communities yet.
I also assume microblogging sites like Mastodon and Pleroma, along with the Prismo link aggregator, can use hashtags as an analogy for communities. While a post on those sites can belong to multiple tags, Lemmy can imitate this with crossposting in multiple communities. Is this reasonable?
PeerTube is where I get more confused, and I'm not alone. As a reply there mentioned, we can view a PeerTube user account, such as https://lemmy.ml/u/thelinuxexperiment@tilvids.com and https://lemmy.ml/c/h3h3productions@h3h3.club , although it doesn't seem to work for framatube.org.
However the interfaces of Lemmy and PeerTube are radically different, as PeerTube is foremost a video hosting site and Lemmy is a link aggregator. I think it's fair to assert that a Lemmy post cannot be displayed on a PeerTube instance without hacks no-one wants, which leaves PeerTube->Lemmy posting, and mutual liking/commenting/reporting/etc.. A PeerTube video can be adapted as a link post in Lemmy. I'm not certain how a PeerTube upload would signal which communities it should be posted to in Lemmy, but there are reasonable options like an extra field in the upload settings, or a link in the description.
Question 2: Is there a plan to have anything more than PeerTube creating link posts in Lemmy communities with federation between comment sections?
Trying to learn the current situation in order to ask good questions has taught me a lot, I was in a mindset that we had to be able to make posts on other sites in order to usefully federate, when that isn't really our role as a link aggregator site. Media sites can usefully post to here with federated voting and comment sections.
I am trying stuff right now and must say lemmy seems not jet well integrated into the fediverse. I searched for a post I wanted to comment on on mastodon.social. Yes, i found it and could comment it on mastodon, but it did not show on lemmy. I do not know if there is some kind of moderation which I have to await, but it is definetly not seamless. Likewise, how do one interact with other lemmy instances? I did not find a way to communicate over instance-borders. If somebody has more experience / insight into this, please help.
So, there's a simple constraint built into the fediverse or decentralised social media: each separate instance or node does not have a copy of everything on the fediverse. Instead, each instance only has a copy of the things that its users directly follow or subscribe to.
Often this is described as what an instance can (or cannot) see.
In your case, you were probably searching for things that lemmy.ml just can't see or hasn't yet seen.
For lemmy in general, and I'm hazy on this TBH, this will apply to communities. That is, an instance won't have the content of a community unless one of its users has subscribed to it. When you search for communities though, any community from any instance that connects to lemmy.ml will turn up (AFAIU).
For mastodon content, when viewed from lemmy.ml, not much is going to turn up here because lemmy isn't about following or subscribing to individuals. No one on lemmy.ml is following the mastodon user you were searching, because they can't. And so the post you were searching for just isn't visible to lemmy.ml.
The only way in which a mastodon post is visible from lemmy is when that post is directly addressed to lemmy either as a post to a lemmy community or in reply to a lemmy post or comment.
This is actually quite easy to do from mastodon, in large part because both lemmy communities and users are presented to mastodon as though they are other users. As things are now, lemmy doesn't treat mastodon users as something similar to a community that you can subscribe to, that's not really what lemmy is about.
So yes, not everything is seamless here on the fediverse, and in principle I'm with you: there's some maturation yet to occur and it's honestly best to think of this place as a big prototype.
Personally, I don't think this is the fault of the platform developers, as they're doing what they can with the protocol and software available to them. The space that is, IMO, most fertile for growth and innovation is in the clients/apps, where multiple platforms can be woven together into a single interface in much the same way that a single email app can help you manage multiple email accounts. So far, to be fair, much of the activity in this space has been dedicated to trying to mimic the success of Twitter apps. Not much true innovation has taken off yet.
Additionally, there's almost certainly some work to be done in adding and developing sort of "middleware" software and services across the fediverse.
Thank you for this elaborate response. I did not want to imply any wrongdoings on the developers side, I am just starting making sense of all this. So, how do i subscribe to e.g. https://beehaw.org/c/creative while using lemmy.ml?
Never mind, found out myself.