feat: the opt-in rematch state, the lobby's auto-rematch flag and its switch (v0.21.0)

[cycle-five]

Design

Rematch tuning (workspace spec docs/superpowers/specs/2026-10-15-rematch-tuning-design.md, owner-approved 2026-10-15; plan docs/superpowers/plans/2026-10-15-rematch-tuning.md, Task 1).

On 2026-10-15 in prod, 13 of the 25 cancelled games lived under 60 s. Most were rematches auto-started for a lone player who was leaving. Backend v0.48.0 will:

• make the countdown 30 s;
• give each lobby an auto-rematch switch (off = opt-in Play Again, D1/D2/D5);
• never start a rematch below 2 players (D3′).

This PR is the wire contract for that. Every change is additive.

Change (v0.20.0 → v0.21.0)

• RematchCountdownState::OptIn { ready, eligible, needed, game_type } (status: "opt_in"). Ids are strings (DisplayFromStr), like Active.player_ids.
• LobbyChange::AutoRematchChanged { enabled, changed_by } (change_type: "auto_rematch_changed"), sent inside the existing LobbyDelta.
• LobbySnapshot.auto_rematch: bool with #[serde(default = "default_true")], so a snapshot from an older server reads as on.
• ClientMessage::SetAutoRematch { enabled } (type: "set_auto_rematch"), with requires_lobby() == true.

Compatibility

• Old backend + new consumers: auto_rematch defaults to true, and OptIn is never produced.
• New backend + old frontend: OptIn cannot reach an old client. Lobbies start with auto-rematch on, and an old client has no switch to turn it off. A stray one falls into rematch-countdown.ts's default branch (spec, "Compatibility and release").

Tests

There are serde round-trips for:

• OptIn, with string ids and the opt_in tag;
• AutoRematchChanged, checked against exact JSON;
• LobbySnapshot, with auto_rematch absent (reads as on) and with it present;
• SetAutoRematch: parse, message_type() and requires_lobby().

cargo test passes (106 unit tests plus doctests), and clippy and cargo +nightly fmt are clean.

Review: there is no automated reviewer on this repo (SDLC step 7). The task was reviewed by an independent reviewer pass against the spec's exact wire names, with no findings.

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https://claude.ai/code/session_01THikdM3Ru6UrrVU7DMcwBY