Sync: add rest_api_allowed_public_metadata data to the whitelist.

Currently we don't sync the rest_api_allowed_public_metadata (we sync the whitelist) but not the data. We should add the info into the whitelist. So that we can rebuild the api endpoint in the future.

cc: @lezama Thoughts?

Start by locating the sync whitelist and the rest_api_allowed_public_metadata data it currently omits. Trace how the whitelist is rebuilt or consumed, then verify that the metadata is included so the API endpoint can be rebuilt in the future.

Written by the indexing model from the issue text.