Blockquote does not work in markdown format. The symbol (great than) is simply ignored.
It works as expected on MoodleCloud but the issue can be replicated on Moodle.org forum posts and on self-hosted Moodle sites.
The original query about this came via Moodle.org community forums - https://moodle.org/mod/forum/discuss.php?d=385622 and screenshots of the working code on MoodleCloud is visible in that thread. The OP suggests that this is an issue from 3.4 onwards.
NOTE: this is markdown format, not the HTML editor but I cannot create the issue without choosing a component!