Should a meta_key or other key-value table columns use a HASH or BTREE index?
That's the wrong question.  The indexes that WP provides on the meta tables are inefficient.  (And the general EAV pattern sucks.)
This explains how to significantly improve the indexes:  http://mysql.rjweb.org/doc.php/index_cookbook_mysql#speeding_up_wp_postmeta
Back to your question:  BTree is about as fast as Hash (were it to exist).  And Hash is not available for InnoDB.  (InnoDB is the only 'engine' you should use for WP.)
I believe that the developer of InnoDB saw that &quot;one side does fit all&quot; when he implemented only BTree.