Synapse accepts optional unspecced `servers` field in `PUT directory/room/{roomAlias}`

This issue has been migrated from [#14177](https://github.com/matrix-org/synapse/issues/14177).

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Spec: https://spec.matrix.org/v1.4/client-server-api/#put_matrixclientv3directoryroomroomalias

https://github.com/matrix-org/synapse/blob/6b99a66fe0260682fa95a0b19d3bee19c1e48876/synapse/rest/client/directory.py#L74-L89

Forwarded to here https://github.com/matrix-org/synapse/blob/1a209efdb2a6c51e52dd277de7581099852877ae/synapse/handlers/directory.py#L173 and to here https://github.com/matrix-org/synapse/blob/1a209efdb2a6c51e52dd277de7581099852877ae/synapse/handlers/directory.py#L93-L95 and eventually written to the database here https://github.com/matrix-org/synapse/blob/3e0536cd2afb5a640619bd872fc27b068ec3eb9b/synapse/storage/databases/main/directory.py#L112-L117

Start with the PUT room-alias handling in synapse/rest/client/directory.py, then follow the references into synapse/handlers/directory.py and synapse/storage/databases/main/directory.py. Compare the accepted request fields with the linked Matrix specification and trace where servers is persisted. Done means the endpoint behavior matches the specification and the unspecced field is no longer accepted or stored.

Written by the indexing model from the issue text.