Inconsistenly using pre-stored params for UI auth

This issue has been migrated from [#8968](https://github.com/matrix-org/synapse/issues/8968).

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We have two methods from the handler that get called on each request to complete UI auth, the aptly named [`validate_user_via_ui_auth`](https://github.com/matrix-org/synapse/blob/c9c1c9d82f190abc2f1254f75fe42bf29eff08e1/synapse/handlers/auth.py#L279-L325) and a lower-level method: [`check_ui_auth`](https://github.com/matrix-org/synapse/blob/c9c1c9d82f190abc2f1254f75fe42bf29eff08e1/synapse/handlers/auth.py#L407-L453).

All endpoints call `validate_user_via_ui_auth` (which calls `check_ui_auth` under the hood) except those that don't yet have an known requester (register and password reset) which directly call `check_ui_auth`.

Per matrix-org/matrix-doc#2907, the parameters of the original request to UI auth get persisted and only need to be provided once to Synapse. Unfortunately it seems that most of the endpoints which call `validate_user_via_ui_auth` completely disregard this and ignore the return values, using only the parameters from the most recent request.