Federation of Server Discovery

This issue has been migrated from [#10169](https://github.com/matrix-org/synapse/issues/10169).

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Feature: Enabling sharing of servers listed in the server dropdown in the room discovery window through federation.

One possible way of implementing this would be to allow server owners to maintain a "default server list" of servers they want displayed to their users, as well as a "follow list" of servers whose default server lists they want to append to their own default server list (minus duplicates). Element would get the list of servers from the homeserver it is connected to. Blacklisted servers would not be shown in the dropdown of course.

Each server in the "default server list" could have a description as well, which can either be defined by the server owner, or if undefined could be pulled directly from the server that is linked to.

(On this same note, the server dropdown in element has to be ditched for a different UI, when you have many servers it is awful).

Hope this makes sense, cheers!

The issue names no Synapse files, tests, or entry points. Start by locating the existing room-discovery server-list implementation and federation APIs, then determine the scope for sharing default and follow lists, descriptions, and blacklist handling. Done would require an agreed design, implementation boundaries, and tests for the federated list behavior.

Written by the indexing model from the issue text.