I've run into this bug while switching all my sh/bash scripts to rc and
used the following workaround:

    (defun my-sh-set-shell-hook ()
      (when (member sh-shell '(rc es))
        (modify-syntax-entry ?` ".")))
    
    (add-hook 'sh-set-shell-hook 'my-sh-set-shell-hook)

I doubt this warrants inclusion into sh-script.el as is, but should
demonstrate a possible approach how to fix it.