`age` logic for events is broken

This issue has been migrated from [#8429](https://github.com/matrix-org/synapse/issues/8429).

---

There is a bunch of code inside synapse which tries to add an ~~unspecced~~ `age` field to events.

The intention of such a field is to try to mitigate problems with incorrectly-set clocks. Rather than saying "this event was created at 12:00", we can say "this event was created 10 minutes ago"; for certain applications (notably VoIP signalling), that information is more useful. ~~It would be more useful still if it was actually specced, but that's a side-issue.~~

Considering a flow from client to client over federation, I think the intention of the implementation is this:
* Server A receives event from sending client. It records its best estimate of the timestamp the client created the event (typically the time it received the request from the client) in a field in the event called `age_ts`.
* Server A creates a transaction including the event to send to server B. Just before it sends that transaction over the wire, it removes `age_ts` from the event and replaces it with a raw `age` field giving the number of milliseconds that have elapsed since `age_ts`.
* Server B receives the transaction, and recreates `age_ts` based on the time it received the transaction.
* Server B formats the event for a client, and replaces `age_ts` with `age`.

Assuming that a given server's clock is *consistently* inaccurate, it is kinda plausible, though obviously it neglects any delays between formatting transactions and them being received at the destination.

However, I suspect it doesn't actually work. The C-S code in synapse stores `age_ts` in the `unsigned` property of the event (~~which is probably correct~~ no, we have `internal_metadata` for this sort of thing); however, the logic in the federation sender which tries to replace `age_ts` actually looks for the property in the top level of the event rather than in `unsigned`. It therefore leaves `age_ts` in place in `unsigned`. The federation receiver logic will accept an `age` in *either* `unsigned` or at the top level, and replaces it with an `age_ts` at the *top level*. The C-S code doesn't know to strip it out of there, which means it leaks out to the C-S API (see https://github.com/matrix-org/matrix-doc/issues/2685).

This has clearly been broken for ages, and nobody has really noticed. ~~Given none of it is specced, I am inclined to say that we should strip it all out.~~ (Update 2023/01/17: it's specced nowadays.)