The qualifier for Endfield characters should be *_(arknights). It should only be *_(arknights:_endfield) if we somehow need to distinguish the Endfield version of a character from the original version of the character.
This follows precedence from other series such as Fate, where we use the name of the overall franchise as the default qualifier, and we only use the name of a specific game as a qualifier when a character appears in multiple games, and we need to specify which game they're from. For example, we have Nero Claudius (Fate/Extra) for the version of Nero Claudius from Fate/Extra, and Nero Claudius (Fate) for Nero Claudius in general. We don't have Nero Claudius (Extra) (Fate) or Nero Claudius (Fate) (Extra). For other characters we just have *_(Fate) unless we're talking about a specific version of a character from a specific game.
In general, when a game becomes a franchise, use the franchise name as the qualifier, not the game a character first appears in. Which game a character first appears in usually becomes irrelevant over time. See: Touhou.
And we don't need an Arknight (series) tag as long as 99.9% of it is the original game. Arknights has 139k posts and Arknights: Endfield has ~500 posts. It just creates tag bloat when every Arknights post gets an extra Arknights (series) tag that's identical to the first game. It's too premature to do this when Endfield isn't even officially out yet.
We made this mistake with Overwatch when Overwatch 2 was first announced. We split the Overwatch tag up into Overwatch 1 and Overwatch 2, but there turned out to be no significant difference between Overwatch 1 and 2. So now every Overwatch post gets multiple copyright tags, even though nobody actually searches for Overwatch 1 or Overwatch 2. All the search traffic is just for Overwatch, because that's what the game is called and nobody really cares about the distinction between the two.