The Vim plug-in Matchit (see :help matchit-intro) comes bundled with Vim (see :help matchit-install) and makes it possible to extend the pairs between which hitting % lets the cursor jump. (An alternative more recent drop-in replacement is Matchup.)

You can make sure that the most recent version of it is loaded by adding the lines

" Load matchit.vim, but only if the user hasn't installed a newer version.
if !exists('g:loaded_matchit') && findfile('plugin/matchit.vim', &rtp) ==# ''
  runtime! macros/matchit.vim
endif

to your vimrc, as vim-sensible does.

Though :help 'matchpairs' says that Only character pairs are allowed that are different, thus you cannot jump between two double quotes., there are heuristics (depending on the file type) such as white space before or after a delimiter (in prose) that can work around that restriction; never completely, but in practice sufficiently.

This repository adds these heuristic settings for common prose markup file types such as

• markdown / pandoc,
• latex,
• asciidoc,
• rst, and
• plain text.