Several write operations still occur on the main process when `/register` is routed to workers

This issue has been migrated from [#13379](https://github.com/matrix-org/synapse/issues/13379).

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It's possible to route [`POST /_matrix/client/v3/register`](https://spec.matrix.org/v1.3/client-server-api/#post_matrixclientv3register) to workers. This allows offloading most of the work involved in registration to the main process. A few operations occur on the main process ([here](https://github.com/matrix-org/synapse/blob/92103cb2c8b8bff6b522a7bfa8a3a776b4821b11/synapse/handlers/register.py#L683-L742) is where the logic splits between worker and main process):

https://github.com/matrix-org/synapse/blob/53b77b203ac12f20a6534393464588d5d49435f5/synapse/storage/databases/main/registration.py#L2103-L2191

I *think* the only operation in this method that can't currently be completed by a worker is: https://github.com/matrix-org/synapse/blob/53b77b203ac12f20a6534393464588d5d49435f5/synapse/storage/databases/main/registration.py#L2186-L2189

But the rest could potentially be delegated to the worker process.

I don't believe that these operations are particularly resource intensive.

Start with the split in synapse/handlers/register.py at lines 683-742, then inspect synapse/storage/databases/main/registration.py lines 2103-2191. Identify which registration writes can be delegated to the worker while preserving the operation at lines 2186-2189 on the main process. Done means worker-routed /register no longer performs the delegable writes on the main process without changing registration behavior.

Written by the indexing model from the issue text.