I was with Ibn 'Abbas, and Ibn 'Abbas saw the Messenger of Allah ﷺ doing like this, and it is also said that the words are: He (the Holy Prophet) offered prayer; and the word" people" is not mentioned.
أَنَّ ابْنَ عَبَّاسٍ شَهِدَ ذَلِكَ مِنَ النَّبِيِّ ﷺ وَقَالَ صَلَّى وَلَمَ يَقُلْ بِالنَّاسِ