In the bracha right before the Amidah during Shacharis, Nusach Ashkenaz and many variations of Nusach Sefard have:
שִׁירָה חֲדָשָׁה שִׁבְּחוּ גְאוּלִים לְשִׁמְךָ עַל שפַת הַיָּם. יַחַד כֻּלָּם הודוּ וְהִמְלִיכוּ וְאְָמְרוּ: ה' יִמְלךְ לְעולָם וָעֶד: צוּר יִשרָאֵל. קוּמָה בְּעֶזְרַת יִשרָאֵל. וּפְדֵה כִנְאֻמֶךָ יְהוּדָה וְיִשרָאֵל. וְנֶאֱמַר[וְנֶאֱמַר:] גּאֲלֵנוּ ה' צְבָאות שְׁמו קְדושׁ יִשרָאֵל: בָּרוּךְ אַתָּה ה', גָּאַל יִשרָאֵל
However, the Chabad nusach and Nusach Edot Hamizrach omit the bolded words. Since nusach Chabad is techincally a variation Nusach Sefard, why is "Tzur Yisroel" omitted from the text?
Additionally, is this just in Nusach Chabad or do other Nusach Sefard versions omit these words? All of the "universal" (not belonging to a particular Chasdic dynasty or Rebbe) Sefard siddurim I've seen and davened from included the words.