Run lobbies' games on the server

The server now runs every lobby's sandbox and queued games as rooms, stepped at
the tick rate on one thread. Players send controls ahead of time, late ones repeat
their last, and everyone in a room gets back the controls it played, its events
and checksums. Games start from sandbox queues, players return when they leave,
and play-again moves them to a fresh room. Protocol version 3.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

src/protocol.h

@@ -27,7 +27,7 @@
 #include <string_view>
 #include <type_traits>
 
-constexpr int PROTOCOL_VERSION = 2;
+constexpr int PROTOCOL_VERSION = 3;
 constexpr int LOBBY_MEMBERS_MAX = 4;
 constexpr int LOBBY_CODE_LENGTH = 4;
 // Letters only, without I and O, so codes are easy to read out and type.
@@ -38,6 +38,41 @@ constexpr int KICK_REASON_MAX = 60;
 constexpr const char SERVER_URL_DEFAULT[] = "wss://shweetz.net/smack-a-brother/ws";
 constexpr int SERVER_URL_LENGTH = 128;
 
+// Binary messages between a game and the server once it's in a lobby, each starting with its type. A room is one
+// online game (a lobby's sandbox, or a game queued in it), numbered by the server.
+//
+// Game to server:
+//   PACKET_PROFILE   Profile                                    the fighter this player brings into the lobby
+//   PACKET_INPUTS    room, ack, first, Uint16 count, Controls*  this player's controls from a tick on, and the last
+//                                                               tick it has confirmed
+//   PACKET_QUEUE     Uint8 isOpen, Rules                        queue a game in the sandbox, or stop queueing it
+//   PACKET_CHAT      Uint16 length, text
+//   PACKET_TYPING    Uint8 isTyping
+//   PACKET_RENAME    Uint16 length, text
+//
+// Server to game:
+//   PACKET_STATE     room, tick, state                          the game this player is in now, as a tick starts
+//   PACKET_EVENT     room, serial, RoomEvent                    the room's events, numbered from 0, in order
+//   PACKET_FRAMES    room, lead, first, Uint16 count, then for each tick: Uint16 events, Uint8 fighters, Controls*
+//                                                               every fighter's controls as the server played them,
+//                                                               once the events before them are in, and how early
+//                                                               (in ticks) this player's last controls came
+//   PACKET_CHECKSUM  room, tick, Uint32                         the room's state as that tick starts
+//   PACKET_CHAT      from, Uint16 length, text                  and the same for typing and renames
+enum PacketType : unsigned char
+{
+    PACKET_PROFILE = 1,
+    PACKET_INPUTS,
+    PACKET_QUEUE,
+    PACKET_CHAT,
+    PACKET_TYPING,
+    PACKET_RENAME,
+    PACKET_STATE,
+    PACKET_EVENT,
+    PACKET_FRAMES,
+    PACKET_CHECKSUM
+};
+
 // Packets are plain values one after another, as they sit in memory (every platform agrees on these layouts).
 struct PacketWriter
 {