Create a mypy plugin for replication class methods

This issue has been migrated from [#8828](https://github.com/matrix-org/synapse/issues/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](https://github.com/matrix-org/synapse/blob/1781bbe319ce24e8e468f0422519dc5823d8d420/synapse/replication/http/_base.py#L110-L134) in `ReplicationEndpoint`.
* Their signatures differ from `send_request`, which is what is [returned by `make_client`](https://github.com/matrix-org/synapse/blob/2e380f0f1802e5310f5a19b5cac314ce742aaecd/synapse/handlers/e2e_keys.py#L60-L62) and what is run when [making a replication request](https://github.com/matrix-org/synapse/blob/2e380f0f1802e5310f5a19b5cac314ce742aaecd/synapse/handlers/e2e_keys.py#L224-L226).

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](https://github.com/matrix-org/synapse/blob/develop/scripts-dev/mypy_synapse_plugin.py#L31) to properly check the types and remove the need to ignore them.

Note that this issue grew out of a discussion here: https://github.com/matrix-org/synapse/pull/8809#issuecomment-733639886

Start with scripts-dev/mypy_synapse_plugin.py and the ReplicationEndpoint base methods in synapse/replication/http/_base.py. Compare those signatures with _serialize_payload, _handle_request, and send_request in the referenced replication classes and handlers. Done means the plugin checks these method types correctly and the relevant # type: ignore annotations are no longer needed.

Written by the indexing model from the issue text.