Personally I think they should remove the ZedXSyndra interaction by having Syndra ally herself with the Vastaya, only for them to eventually get cut down by the Order of Shadow. It still needs some work, but it'll hopefully have more thematic exploration than Syndra just being another one of Zed's pawns.
I always figured that Syndra would be an imposing political figure in Ionia post invasion and a major advocate for abandoning old, restrictive traditions. Sort of the opposite or Irelia who I figured would be a sort of Ionian traditionalist, hell maybe even someone who you might consider a nationalist, especially after having spent some of her younger years embroiled in conflict for the fate of her lands and people.
I don't know where your information about her being depressed comes from; as far as I remember she's never suffered from depression.
Also there's never been an official Zed and Syndra connection other than the fact they're not so good Ionians. They've never interacted in any lore.
Syndra? A pawn of Zed?
Currently their lore has nothing solid connecting each other beyond fan theories.
And seriously? A pawn? Lore wise I'm not a fan of Syndra but I know she is very powerful and unlikely to be a pawn of Zed. If anything, Zed would try to stay clear of her if he cannot make her an ally, and that's Syndra would ever consider since that last time she was subservient she ended up painting the walls red with the blood of her teacher.
I don't think Syndra is one of Zed's pawns
