The answer to this is from two angles:
The first: we have a very clear text showing that he ﷺ did not perform Friday Prayer while travelling. This occurred on the Day of ‘Arafah, which fell on a Friday during the Farewell Pilgrimage. In Sahih Muslim, in the hadith of Jabir, it is related that when the Prophet ﷺ reached the bottom of the valley on the Day of ‘Arafah, he dismounted and delivered a sermon to the people. Then, after the sermon, Bilal gave the call to prayer; he then gave the iqamah, and the Prophet ﷺ prayed Zuhr. Then he gave the iqamah, and he ﷺ prayed ‘Asr. (1)
This manner differs from Friday Prayer in several respects:
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In Friday Prayer, the sermon comes after the call to prayer, whereas here the sermon came before the call to prayer.
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Friday Prayer is preceded by two sermons, while the hadith of Jabir mentions only one sermon.
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The recitation in Friday Prayer is audible, whereas the hadith of Jabir indicates that he ﷺ did not recite aloud, since it states: “He prayed Zuhr; then he gave the iqamah and prayed ‘Asr.”
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Friday Prayer is called Friday Prayer, whereas the hadith of Jabir states: “He prayed Zuhr.”
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‘Asr is not combined with Friday Prayer, whereas the hadith of Jabir states: “He prayed Zuhr; then he gave the iqamah and prayed ‘Asr.” This is an explicit and clear proof: in this great gathering, whose Muslims would disperse to their respective lands and say, “We prayed Zuhr with the Messenger of Allah ﷺ on Friday,” it provides definitive evidence that the traveller does not perform Friday Prayer.
The second: if the Prophet ﷺ used to perform Friday Prayer during his journeys—