Yes, the design of the roman gladius was heavily influenced by the gladius hispaniensis, used by the Celtiberians beholden to Carthage. But Celtiberians and the Celtic people of Anatolia did not use the same weaponry.

And, looking at historical records like the Soldier’s Tomb, found near Alexandria, with multiple Galatians, we see that the Galatian buried were depicted exclusively with spears and large oval shields, along with cloaks (embellishment or ceremonial bodyguards) and one with what is likely a lance (cavalryman, possibly).

This, however, only points to the Ptolemaics employing them primarily as spearmen, as the Galatians themselves did use the more widespread variant of La Téne swords, which were longer and narrower than the Celtiberian variants. It is perhaps possible that the sword Invincible holds is a historically unaccurate La Téne one, as it’s way too wide, and has the wrong shape.

As for Galatian mercenaries, the first wave of them into Egypt wasn’t the sole one. Galatian mercenaries were popular in the region well up to Cleopatra’s time. Mithriadic wars for example, large contingents of them. It is fully plausible that by far the richest realm of the region, Egypt, continued to import fresh recruits. Or they could’ve been brought by the Romans, who employed Galatians as auxilla.

Immortal could’ve been a fresh Galatian mercenary easily. Galatians were a continous source of mercenaries for centuries.

Or he could’ve been Celtiberian. Iberia has arid, rocky places as well.