If I use Entei V's "Fleet Footed" Ability and retreat it for another one on my bench, can I use the new Entei V's "Fleet Footed" Ability too?
Yes, you can. Once per turn applies to the Pokemon that uses the Ability.
Source: Brilliant Stars FAQ; TPCi Rules Team (2022-02-24)

Relevant cards

Note: All applicable cards may not be listed below.
SWSH9_22
SWSH9_22