There is an existing proposal to migrate Wikiquote to a structured, multilingual Wikiquote utilizing MediaWiki-extensions-WikibaseRepository.
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For what it's worth, I've tried experimenting with this on test.d but I haven't had any luck thinking thru what exactly would be needed or how it would be implemented. If someone has feedback and wants to collaborate, please let me know.
Create items similar to Wikidata to contain quotations and then add properties like source, translation, citation information, etc.
This is a tracking task so probably many more subtasks should be created (I honestly haven't even looked at what would be involved in doing this). I created the task as a starting point because I couldn't find a Phabricator task for the proposal. I started looking into this because of T187900.
I'm sorting out the hackathon 2018 board (on which this task is) and well described tasks generally have a higher chance of actually being worked on. Might not be the best board for a tracker task.
Feel free to remove it. :) I might try and figure out what would be involved during the Hackathon.