Servers can end up on a long backoff and may not have an excuse to poke each other to be 'woken'

This issue has been migrated from [#8346](https://github.com/matrix-org/synapse/issues/8346).

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My recent work involving Catch-up after Federation is all well and good, but one little thing remains that niggles me a bit:

If a (probably) small server goes offline for a while, other servers will more or less give up on it — it will get a long backoff.

If that server ever comes online again, other servers won't retry sending to it for either a long time, or until they hear from that server in the first place.

Problem is, 'hearing' from that server may not happen if there is nothing to be heard about — presence EDUs are a good excuse for a transaction (which is kind of funny when a user sees all their rooms backfill as they log in, but oh well) but some servers have presence disabled.

I guess we want some way of making our server poke others to let them know we are online.

Problems with this:

- when?
- how? (empty `/send`?)
- This seems to be very Synapse-centric — i.e. it kind of relies on knowing that Synapse will 'wake' us if we poke it — but other server implementations may act differently. I guess it would want some spec recommendations...

The issue names no files, tests, or entry points. Start by reading Synapse's federation catch-up and server backoff behavior, then determine when and how an online server should notify peers, including whether an empty /send is appropriate. Done means the timing and mechanism are defined, with any needed Matrix federation specification recommendations.

Written by the indexing model from the issue text.