Add the shared schemas for the quiz request/response cycle, defining
the contract between the API and the frontend.
- Reorganise packages/shared: move schemas into a schemas/ subdirectory
grouped by domain. Delete the old flat schema.ts.
- Add AnswerOption, GameQuestion, GameSession, AnswerSubmission, and
AnswerResult alongside the existing GameRequest.
- optionId is an integer 0-3 (positional, shuffled at session-build
time so position carries no information).
- questionId and sessionId are UUIDs (globally unique, opaque, natural
keys for Valkey storage later).
- gloss is rather than optional, for a predictable
shape on the frontend.
- options array enforced to exactly 4 elements at the schema level.
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