Both quote blocks can take advantage of nested blocks. This is necessary to allow blocks other than paragraphs inside the quote content, e.g. a list or a heading. It would also enable us to simplify RichText down the road.

I've implemented this before in #6520, but it was closed because the nested blocks UI didn't seem good enough at the time (cc @jasmussen to check if it is now), and the PR has gotten too old to rebase. I suspect a lot of things can reused from it.