Yes, incremental search does not move the position of the point, so yank does not copy the match.
The simplest solution is probably the following:
Define a function that copies the search match:
(defun copy-isearch-match () (interactive) (copy-region-as-kill isearch-other-end (point)))
And add it to the search mode map
(define-key isearch-mode-map (kbd "Mw") 'copy-isearch-match)
Then by doing Mx isearch-forward-regexp , you can press Mw to copy the match.
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