I think we’re getting into “what is a/the puzzle” territory. In that position I would imagine one way it could be phrase is “Black to live”, and after the first correct move black is alive, either with points if Black moves again or in seki if White chooses to make it.
But there’s no forced continuation of the puzzle for White, White can tenuki since Black achieved their goal, so really it’s life in gote.
If the Black move is already played, maybe the puzzle would read be “White to make a seki” which as you mentioned would be a gote seki for White.
I just think the idea of a sente seki for the ‘Defending player’ seems a bit odd, without examples . On the one hand if it’s a seki either there’s already two groups which could both be captured that end up a seki (in which case who’s the defender? the person who plays second? ), or like in your example instead it could be a new group created inside that lives in seki, and it seems like the person creating the group inside is probably the attacker.