Allow sending presence only to whitelisted servers or keeping it local only

[matrixbot]

This issue has been migrated from #8055.

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As written in #3971, sending presence tends to slow down servers with little resources. A known workaround is to disable presence on the server, but there is no option other than enabling and disabling all presence. In the discussion for #3971 @jpulley and @MurzNN mentioned another possible option:

Other possible workaround - make option in Synapse to disable sending presence for all federated users, or whitelist of servers to which send presence

This is something I'd love to see, personally. I want presence on my homeservers and on my friends' but I don't want it at all on the big matrix.org rooms. I would also love to be able to do something like disable presence for any room with more than X members.

Not only it helps with reducing load on the server while allowing some users to share their presence info, but I think it has privacy implications as well: Users might not want to tell everyone when they are online, just share it with friends/colleagues/collaborators on the same server or a few other. (It is now possible to have two servers: a "public" one with presence disabled, and a "private" one that would send presence, but one would not join big rooms from it. But that would be confusing and user-unfriendly.)

Therefore I think this should be implemented regardless of how #3971 is fixed.