Does the pokemon verse distinguish from actual named physical pokemon moves and a pokemon who decides to do physical activity?
Besides the above mentioned Run Away, some forms of movement (Levitate), are Abilities rather than moves. Wimp Out is also an Ability, the execution of which involves movement, albeit, based on cowardice.
IIRC. In some games, it has been possible for Wild Pokemon to flee, but I don't know if any of them can do that against Eternatus, & it's questionable if it was an intended scenario for Eternatus, since I don't know if Wild Pokemon running away is in Sw/Sh, which is where Eternatus's ability is shown.
In theory, you can flee, but Eternatus itself is a Wild Pokemon being battled by trainers; Presumably, the Trainers recall their Pokemon when fleeing, since we don't see it happen, but MOST games don't have trainers' Pokemon present in the overworld/when not in battle, & Sw/Sh is a game where your Pokemon aren't out of their Poke Balls when not in battle.
So it MIGHT be that Eternatus was supressing the Pokemon but not the trainers, & thus the trainers flee, & presumably, recall their Pokemon to do so. Especially so if we're able to switch against Eternatus, but I dunno if we can.
That said, I have no idea if this isn't game mechanics; Letting players run from story-mandatory legendary battles is a thing in several recent games.