Matrix servers keep a copy of any remote room an account on the server has joined, and it’s possible to recreate a room from the copies held on different servers. There are more details I don’t remember, but at a high level that’s how it’s distributed.
Storing messages of remote rooms in addition to local rooms is why people complain about the storage requirements of Matrix servers. They don’t realize it’s distributed.
How is the puppy?
As for interoperability between services… Monetization of surveillance data. The social media companies are Ad companies, and they make their money surveilling people and selling access. It’s harder to build an accurate model of a person when only pieces of data is available, and they need to have more data then the other Ad tech companies they’re competing with.