Justifying (or Rejecting) a New Store

A team running Postgres for their product catalogue proposes adding Elasticsearch "because search will be faster" and MongoDB "because it's more flexible for the catalogue," in the same sprint.

1. Evaluate each proposal: is it justified, and by what specific requirement?
2. For the proposal(s) you accept, describe how the new store stays in sync with Postgres and what staleness is acceptable.
3. What questions would you ask before approving either addition?