Create a mypy plugin for replication class methods

[matrixbot]

This issue has been migrated from #8828.

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Replication servlet classes, such as ReplicationRemoteJoinRestServlet, ReplicationUserDevicesResyncRestServlet etc. each have _serialize_payload and _handle_request methods. Traditionally we haven't added typing to these methods as it breaks mypy for two reasons:

• Their signatures differ from the base methods in ReplicationEndpoint.
• Their signatures differ from send_request, which is what is returned by make_client and what is run when making a replication request.

If types are added to any instance of _serialize_payload or _handle_request, mypy will complain about this discrepancy, and thus an # type: ignore has typically been put on the method signature in order to avoid this:

https://github.com/matrix-org/synapse/blob/377673db2ac4b4af6a237252dc39cf464cfb3a30/synapse/replication/http/membership.py#L55-L62

A better solution is to write a mypy plugin, much like we already have for cache functions to properly check the types and remove the need to ignore them.

Note that this issue grew out of a discussion here: matrix-org/synapse#8809 (comment)