https://misskey-hub.net/ns#_misskey_quote type has not been standardized yet. I think this relation type and other things related to quotes (such as quotes collection) should be specified in a separate FEP.
>note that Misskey doesn't support it (both incoming and outgoing)
Yes, but Misskey and Pleroma support quoteUrl property (IIRC it is defined as as:quoteUrl). FEP-e232 + quoteUrl should work everywhere