Gathering performance data of synapse deployments

This issue has been migrated from [#4659](https://github.com/matrix-org/synapse/issues/4659).

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**Description:**

It would be nice if we could gather some performance information about synapse deployments.

**Short-Term:**

Use a google doc or something similar to allow admins that are willing to contribute the data of their deployments. This data is mostly subjective and depends on a lot of unknowns (like how many users are in which federated channels) but it might still give people who are thinking about setting up a HS a starting point for what to expect. I am hoping these unknowns will, at least somewhat, average out with enough contributions.

Also new admins might not even know how many users they can expect to use federated channels, so having these unknowns in the averages might even be a good thing.

I have drafted up a quick google doc to show you what I mean. It is public so any synapse admin can already contribute. Just keep in mind that this document might be changed, hosted somewhere else or just flat out discontinued entirely at any point.
https://docs.google.com/spreadsheets/d/1hOOh_GK3cvzVFprfP_rWwhNe8ChBqFfJBqIz-36Hhac/edit?usp=sharing

The measurement type "Official Script" is meant for some sort of official script that may gather performance information over say 24 hours or so and average the data as well as detect peaks and so on. I think especially interesting is the column "CPU-Time per Hour" which is almost impossible to do by hand.

**Long-Term:**

Maybe add a diagnostics API to synapse that can be used to make the aforementioned unknowns known in order to give a more accurate performance reading.

Maybe even some opt-**in** anonymous analytics that would be transmitted to a matrix.org hosted server.

**Long-long-Term:**

Maybe even add this API to the matrix specs so people can properly compare different HS implementations.